Search results for: Chebyshev polynomials

Authors: Natalia D. Vaysfel’d, Zinaida Y. Zhuravlova

Abstract:

The loaded plane elastic semistrip, the lateral boundaries of which are fixed, is considered. The integral transformations are applied directly to Lame’s equations. It leads to one dimensional boundary value problem in the transformations’ domain which is formulated as a vector one. With the help of the matrix differential calculation’s apparatus and apparatus of Green matrix function the exact solution of a vector problem is constructed. After the satisfying the boundary condition at the semi strip’s edge the problem is reduced to the solving of the integral singular equation with regard of the unknown stress at the semis trip’s edge. The equation is solved with the orthogonal polynomials method that takes into consideration the real singularities of the solution at the ends of integration interval. The normal stress at the edge of the semis trip were calculated and analyzed.

Keywords: semi strip, Green's Matrix, fourier transformation, orthogonal polynomials method

Procedia PDF Downloads 401

Authors: M. Fakharian, M. I. Khodakarami

Abstract:

In this paper, a new trend for improvement in semi-analytical method based on scale boundaries in order to solve the 2D elastodynamic problems is provided. In this regard, only the boundaries of the problem domain discretization are by specific sub-parametric elements. Mapping functions are uses as a class of higher-order Lagrange polynomials, special shape functions, Gauss-Lobatto -Legendre numerical integration, and the integral form of the weighted residual method, the matrix is diagonal coefficients in the equations of elastodynamic issues. Differences between study conducted and prior research in this paper is in geometry production procedure of the interpolation function and integration of the different is selected. Validity and accuracy of the present method are fully demonstrated through two benchmark problems which are successfully modeled using a few numbers of DOFs. The numerical results agree very well with the analytical solutions and the results from other numerical methods.

Keywords: 2D elastodynamic problems, lagrange polynomials, G-L-Lquadrature, decoupled SBFEM

Procedia PDF Downloads 407

Authors: Min Wang, Sergey Utev

Abstract:

The lessons from the 2007-09 global financial crisis have driven scientific research, which considers the design of new methodologies and financial models in the global market. The quantum mechanics approach was introduced in the unpredictable stock market modeling. One famous quantum tool is Feynman path integral method, which was used to model insurance risk by Tamturk and Utev and adapted to formalize the path-dependent option pricing by Hao and Utev. The research is based on the path-dependent calculation method, which is motivated by the Feynman path integral method. The path calculation can be studied in two ways, one way is to label, and the other is computational. Labeling is a part of the representation of objects, and generating functions can provide many different ways of representing share price paths. In this paper, the recent works on graphical theoretical construction of individual share price path via matroid is presented. Firstly, a study is done on the knowledge of matroid, relationship between lattice path matroid and Tutte polynomials and ways to connect points in the lattice path matroid and Tutte polynomials is suggested. Secondly, It is found that a general binary tree can be validly constructed from a connected lattice path matroid rather than general lattice path matroid. Lastly, it is suggested that there is a way to represent share price paths via a general binary tree, and an algorithm is developed to construct share price paths from general binary trees. A relationship is also provided between lattice integer points and Tutte polynomials of a transversal matroid. Use this way of connection together with the algorithm, a share price path can be constructed from a given connected lattice path matroid.

Keywords: combinatorial construction, graphical representation, matroid, path calculation, share price, Tutte polynomial

Procedia PDF Downloads 105

Authors: Hashem Sazegar

Abstract:

Legendre’s conjecture states that there is a prime number between n^2 and (n + 1)^2 for every positive integer n. In this paper we prove that every composite number between n2 and (n + 1)2 can be written u^2 − v^2 or u^2 − v^2 + u − v that u > 0 and v ≥ 0. Using these result as well as induction and residues (modq) we prove Legendre’s conjecture.

Keywords: bertrand-chebyshev theorem, landau’s problems, goldbach’s conjecture, twin prime, ramanujan proof

Procedia PDF Downloads 329

Authors: Prashant Pandey

Abstract:

In the present article, an effective Laguerre collocation method is used to obtain the approximate solution of a system of coupled fractional-order non-linear reaction-advection-diffusion equation with prescribed initial and boundary conditions. In the proposed scheme, Laguerre polynomials are used together with an operational matrix and collocation method to obtain approximate solutions of the coupled system, so that our proposed model is converted into a system of algebraic equations which can be solved employing the Newton method. The solution profiles of the coupled system are presented graphically for different particular cases. The salient feature of the present article is finding the stability analysis of the proposed method and also the demonstration of the lower variation of solute concentrations with respect to the column length in the fractional-order system compared to the integer-order system. To show the higher efficiency, reliability, and accuracy of the proposed scheme, a comparison between the numerical results of Burger’s coupled system and its existing analytical result is reported. There are high compatibility and consistency between the approximate solution and its exact solution to a higher order of accuracy. The exhibition of error analysis for each case through tables and graphs confirms the super-linearly convergence rate of the proposed method.

Keywords: fractional coupled PDE, stability and convergence analysis, diffusion equation, Laguerre polynomials, spectral method

Procedia PDF Downloads 104

Authors: Samuel Ahamefula Mba

Abstract:

Fluid turbulence is a complex and nonlinear phenomenon that occurs in various natural and industrial processes. Understanding turbulence remains a challenging task due to its intricate nature. One approach to gain insights into turbulence is through the study of entropy, which quantifies the disorder or randomness of a system. This research presents a numerical investigation of entropy signatures in fluid turbulence. The work is to develop a numerical framework to describe and analyse fluid turbulence in terms of entropy. This decomposes the turbulent flow field into different scales, ranging from large energy-containing eddies to small dissipative structures, thus establishing a correlation between entropy and other turbulence statistics. This entropy-based framework provides a powerful tool for understanding the underlying mechanisms driving turbulence and its impact on various phenomena. This work necessitates the derivation of the Poisson equation for pressure transformation of Navier-Stokes equation and using Chebyshev-Finite Difference techniques to effectively resolve it. To carry out the mathematical analysis, consider bounded domains with smooth solutions and non-periodic boundary conditions. To address this, a hybrid computational approach combining direct numerical simulation (DNS) and Large Eddy Simulation with Wall Models (LES-WM) is utilized to perform extensive simulations of turbulent flows. The potential impact ranges from industrial process optimization and improved prediction of weather patterns.

Keywords: turbulence, Navier-Stokes equation, Poisson pressure equation, numerical investigation, Chebyshev-finite difference, hybrid computational approach, large Eddy simulation with wall models, direct numerical simulation

Procedia PDF Downloads 54

Authors: Ravi Kiran Jaladi, Ezz I. El-Masry

Abstract:

Emerging technologies such as ultra-wide band wireless access technology that operate at ultra-low power present several challenges due to their inherent design that limits the use of voltage-mode filters. Therefore, Continuous-time current-mode (CTCM) filters have become very popular in recent times due to the fact they have a wider dynamic range, improved linearity, and extended bandwidth compared to their voltage-mode counterparts. The goal of this research is to develop analog filters which are suitable for the current scaling CMOS technologies. Bulk-driven MOSFET is one of the most popular low power design technique for the existing challenges, while other techniques have obvious shortcomings. In this work, a CTCM Gate-driven (GD) differentiator has been presented with a frequency range from dc to 100MHz which operates at very low supply voltage of 0.7 volts. A novel CTCM Bulk-driven (BD) differentiator has been designed for the first time which reduces the power consumption multiple times that of GD differentiator. These GD and BD differentiator has been simulated using CADENCE TSMC 65nm technology for all the bilinear and biquadratic band-pass frequency responses. These basic building blocks can be used to implement the higher order filters. A 6th order cascade CTCM Chebyshev band-pass filter has been designed using the GD and BD techniques. As a conclusion, a low power GD and BD 6th order chebyshev stagger-tuned band-pass filter was simulated and all the parameters obtained from all the resulting realizations are analyzed and compared. Monte Carlo analysis is performed for both the 6th order filters and the results of sensitivity analysis are presented.

Keywords: bulk-driven (BD), continuous-time current-mode filters (CTCM), gate-driven (GD)

Procedia PDF Downloads 229

Authors: Shubham Jaiswal

Abstract:

During modelling of many physical problems and engineering processes, fractional calculus plays an important role. Those are greatly described by fractional differential equations (FDEs). So a reliable and efficient technique to solve such types of FDEs is needed. In this article, a numerical solution of a class of fractional differential equations namely space fractional order reaction-advection dispersion equations subject to initial and boundary conditions is derived. In the proposed approach shifted Jacobi polynomials are used to approximate the solutions together with shifted Jacobi operational matrix of fractional order and spectral collocation method. The main advantage of this approach is that it converts such problems in the systems of algebraic equations which are easier to be solved. The proposed approach is effective to solve the linear as well as non-linear FDEs. To show the reliability, validity and high accuracy of proposed approach, the numerical results of some illustrative examples are reported, which are compared with the existing analytical results already reported in the literature. The error analysis for each case exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: space fractional order linear/nonlinear reaction-advection diffusion equation, shifted Jacobi polynomials, operational matrix, collocation method, Caputo derivative

Procedia PDF Downloads 415

Authors: Adamu S. Salawu, Ibrahim O. Isah

Abstract:

Direct solution to several forms of fourth-order ordinary differential equations is not easily obtained without first reducing them to a system of first-order equations. Thus, numerical methods are being developed with the underlying techniques in the literature, which seeks to approximate some classes of fourth-order initial value problems with admissible error bounds. Multistep methods present a great advantage of the ease of implementation but with a setback of several functions evaluation for every stage of implementation. However, hybrid methods conventionally show a slightly higher order of truncation for any k-step linear multistep method, with the possibility of obtaining solutions at off mesh points within the interval of solution. In the light of the foregoing, we propose the continuous form of a hybrid multistep method with Chebyshev polynomial as a basis function for the numerical integration of fourth-order initial value problems of ordinary differential equations. The basis function is interpolated and collocated at some points on the interval [0, 2] to yield a system of equations, which is solved to obtain the unknowns of the approximating polynomial. The continuous form obtained, its first and second derivatives are evaluated at carefully chosen points to obtain the proposed block method needed to directly approximate fourth-order initial value problems. The method is analyzed for convergence. Implementation of the method is done by conducting numerical experiments on some test problems. The outcome of the implementation of the method suggests that the method performs well on problems with oscillatory or trigonometric terms since the approximations at several points on the solution domain did not deviate too far from the theoretical solutions. The method also shows better performance compared with an existing hybrid method when implemented on a larger interval of solution.

Keywords: Chebyshev polynomial, collocation, hybrid multistep method, initial value problems, interpolation

Procedia PDF Downloads 97

Authors: Nidal Ali

Abstract:

Consider an algebraic number field K of degree n, A0 K is its ring of integers and a prime number p inert in K. Let F(u1, . . . , un, x) be the generic polynomial of integers of K. We will study in advance the stability of this polynomial and then, we will apply it in order to obtain all the monic irreducible polynomials in Fp[x] of degree d dividing n.

Keywords: generic polynomial, irreducibility, iteration, stability, inert prime, totally ramified

Procedia PDF Downloads 313

Authors: Dimitris Varsamis, Nicholas Karampetakis

Abstract:

It is well known that any interpolating polynomial P(x,y) on the vector space Pn,m of two-variable polynomials with degree less than n in terms of x and less than m in terms of y has various representations that depends on the basis of Pn,m that we select i.e. monomial, Newton and Lagrange basis etc. The aim of this paper is twofold: a) to present transformations between the coordinates of the polynomial P(x,y) in the aforementioned basis and b) to present transformations between these bases.

Keywords: bivariate interpolation polynomial, polynomial basis, transformations, interpolating polynomial

Procedia PDF Downloads 371

Authors: D. Srinivasacharya, Nidhi Humnekar

Abstract:

The goal of this research is to numerically investigate the convection of nanofluid flow in an inclined porous channel. Brownian motion and thermophoresis effects are accounted for by nanofluid. In addition, the flow in the porous region governs Brinkman’s equation. The perturbed state of the generalized eigenvalue problem is obtained using normal mode analysis, and Chebyshev spectral collocation was used to solve this problem. For various values of the governing parameters, the critical wavenumber and critical Rayleigh number are calculated, and preferred modes are identified.

Keywords: Brinkman model, inclined channel, nanofluid, linear stability, porous media

Procedia PDF Downloads 85

Authors: Helmi Temimi

Abstract:

In this paper, we study the super-convergence properties of the discontinuous Galerkin (DG) method applied to one-dimensional mth-order ordinary differential equations without introducing auxiliary variables. We found that nth−derivative of the DG solution exhibits an optimal O (hp+1−n) convergence rates in the L2-norm when p-degree piecewise polynomials with p≥1 are used. We further found that the odd-derivatives and the even derivatives are super convergent, respectively, at the upwind and downwind endpoints.

Keywords: discontinuous, galerkin, superconvergence, higherorder, error, estimates

Procedia PDF Downloads 444

Authors: Said Algarni

Abstract:

The purpose of this study was to investigate selected numerical methods that demonstrate good performance in solving PDEs. We adapted alternative method that involve rational polynomials. Padé time stepping (PTS) method, which is highly stable for the purposes of the present application and is associated with lower computational costs, was applied. Furthermore, PTS was modified for our study which focused on diffusion equations. Numerical runs were conducted to obtain the optimal local error control threshold.

Keywords: Padé time stepping, finite difference, reaction diffusion equation, PDEs

Procedia PDF Downloads 271

Authors: Raj Nandkeolyar, Precious Sibanda

Abstract:

The flow of a viscous, incompressible, and electrically conducting fluid under the influence of aligned magnetic field acting along the direction of fluid flow over an exponentially stretching sheet is investigated numerically. The nonlinear partial differential equations governing the flow model is transformed to a set of nonlinear ordinary differential equations using suitable similarity transformation and the solution is obtained using a local linearization method followed by the Chebyshev spectral collocation method. The effects of various parameters affecting the flow and heat transfer as well as the induced magnetic field are discussed using suitable graphs and tables.

Keywords: aligned magnetic field, exponentially stretching sheet, induced magnetic field, magnetohydrodynamic flow

Procedia PDF Downloads 424

Authors: Abdul Jalil M. Khalaf, Esraa M. Kadhim

Abstract:

The Hosoya polynomial of a graph G is a graphical invariant polynomial that its first derivative at x= 1 is equal to the Wiener index and second derivative at x=1 is equal to the Hyper-Wiener index. In this paper we study the Hosoya polynomial of zero-divisor graphs.

Keywords: Hosoya polynomial, wiener index, Hyper-Wiener index, zero-divisor graphs

Procedia PDF Downloads 489

Authors: Melusi Khumalo, Anastacia Dlamini

Abstract:

In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.

Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations

Procedia PDF Downloads 338

Authors: Kai Zhang, Xi Jiang

Abstract:

Effect of fuel variabilities on premixed combustion of bio-syngas mixtures is of great importance in bio-syngas utilisation. The uncertainties of concentrations of fuel constituents such as H2, CO and CH4 may lead to unpredictable combustion performances, combustion instabilities and hot spots which may deteriorate and damage the combustion hardware. Numerical modelling and simulations can assist in understanding the behaviour of bio-syngas combustion with pre-defined species concentrations, while the evaluation of variabilities of concentrations is expensive. To be more specific, questions such as ‘what is the burning velocity of bio-syngas at specific equivalence ratio?’ have been answered either experimentally or numerically, while questions such as ‘what is the likelihood of burning velocity when precise concentrations of bio-syngas compositions are unknown, but the concentration ranges are pre-described?’ have not yet been answered. Uncertainty quantification (UQ) methods can be used to tackle such questions and assess the effects of fuel compositions. An efficient probabilistic UQ method based on Polynomial Chaos Expansion (PCE) techniques is employed in this study. The method relies on representing random variables (combustion performances) with orthogonal polynomials such as Legendre or Gaussian polynomials. The constructed PCE via Galerkin Projection provides easy access to global sensitivities such as main, joint and total Sobol indices. In this study, impacts of fuel compositions on combustion (adiabatic flame temperature and laminar flame speed) of bio-syngas fuel mixtures are presented invoking this PCE technique at several equivalence ratios. High-pressure effects on bio-syngas combustion instability are obtained using detailed chemical mechanism - the San Diego Mechanism. Guidance on reducing combustion instability from upstream biomass gasification process is provided by quantifying the significant contributions of composition variations to variance of physicochemical properties of bio-syngas combustion. It was found that flame speed is very sensitive to hydrogen variability in bio-syngas, and reducing hydrogen uncertainty from upstream biomass gasification processes can greatly reduce bio-syngas combustion instability. Variation of methane concentration, although thought to be important, has limited impacts on laminar flame instabilities especially for lean combustion. Further studies on the UQ of percentage concentration of hydrogen in bio-syngas can be conducted to guide the safer use of bio-syngas.

Keywords: bio-syngas combustion, clean energy utilisation, fuel variability, PCE, targeted uncertainty reduction, uncertainty quantification

Procedia PDF Downloads 249

Authors: Gennady M. Kulikov, Svetlana V. Plotnikova

Abstract:

This paper focuses on implementation of the sampling surfaces (SaS) method for the three-dimensional (3D) stress analysis of functionally graded (FG) laminated elastic and piezoelectric shells. The SaS formulation is based on choosing inside the nth layer In not equally spaced SaS parallel to the middle surface of the shell in order to introduce the electric potentials and displacements of these surfaces as basic shell variables. Such choice of unknowns permits the presentation of the proposed FG piezoelectric shell formulation in a very compact form. The SaS are located inside each layer at Chebyshev polynomial nodes that improves the convergence of the SaS method significantly. As a result, the SaS formulation can be applied efficiently to 3D solutions for FG piezoelectric laminated shells, which asymptotically approach the exact solutions of piezoelectricity as the number of SaS In goes to infinity.

Keywords: electroelasticity, functionally graded material, laminated piezoelectric shell, sampling surfaces method

Procedia PDF Downloads 656

Authors: Raja Rajeswari K

Abstract:

Orthogonal Frequency Division Multiplexing (OFDM), a multi Carrier transmission technique that has been used in implementing the majority of wireless applications like Wireless Network Protocol Standards (like IEEE 802.11a, IEEE 802.11n), in telecommunications (like LTE, LTE-Advanced) and also in Digital Audio & Video Broadcast standards. The latest research and development in the area of orthogonal frequency division multiplexing, Universal Filtered Multi Carrier (UFMC) & Filtered OFDM (F-OFDM) has attracted lots of attention for wideband wireless communications. In this paper UFMC & F-OFDM system are implemented and comparative analysis are carried out in terms of M-ary QAM modulation scheme over Dolph-chebyshev filter & rectangular window filter and to estimate Bit Error Rate (BER) over Rayleigh fading channel.

Keywords: UFMC, F-OFDM, BER, M-ary QAM

Procedia PDF Downloads 123

Authors: Young Hee Geum

Abstract:

In this paper,we develop the complex dynamics of a family of optimal fourth-order multiple-root solvers and plot their basins of attraction. Mobius conjugacy maps and extraneous fixed points applied to a prototype quadratic polynomial raised to the power of the known integer multiplicity m are investigated. A 300 x 300 uniform grid centered at the origin covering 3 x 3 square region is chosen to visualize the initial values on each basin of attraction in accordance with a coloring scheme based on their dynamical behavior. The illustrative basins of attractions applied to various test polynomials and the corresponding statistical data for convergence are shown to confirm the theoretical convergence.

Keywords: basin of attraction, conjugacy, fourth-order, multiple-root finder

Procedia PDF Downloads 264

Authors: Zainab Al-Maamari, Yassir Dinar

Abstract:

The orbit space of an irreducible representation of a finite group is a variety with the ring of invariant polynomials as a coordinate ring. The invariant ring is a polynomial ring if and only if the representation is a reflection representation. Boris Dubrovin shows that the orbits spaces of irreducible real reflection representations acquire the structure of polynomial Frobenius manifolds. Dubrovin's method was also used to construct different examples of Frobenius manifolds on certain reflection representations. By successfully applying Dubrovin’s method on non-polynomial invariant rings of linear representations of dicyclic groups, it gives some results that magnify the relation between invariant theory and Frobenius manifolds.

Keywords: invariant ring, Frobenius manifold, inversion, representation theory

Procedia PDF Downloads 59

Authors: Jurij Tasinkiewicz

Abstract:

The aim of this work is to present a theoretical analysis of a 2D ultrasound transducer comprised of crossed arrays of metal strips placed on both sides of thin piezoelectric layer (a). Such a structure is capable of electronic beam-steering of generated wave beam both in elevation and azimuth. In this paper, a semi-analytical model of the considered transducer is developed. It is based on generalization of the well-known BIS-expansion method. Specifically, applying the electrostatic approximation, the electric field components on the surface of the layer are expanded into fast converging series of double periodic spatial harmonics with corresponding amplitudes represented by the properly chosen Legendre polynomials. The problem is reduced to numerical solving of certain system of linear equations for unknown expansion coefficients.

Keywords: beamforming, transducer array, BIS-expansion, piezoelectric layer

Procedia PDF Downloads 399

Authors: Nileshkumar Vishnav, Aditya Tatu

Abstract:

A recent approach of representing graph signals and graph filters as polynomials is useful for graph signal processing. In this approach, the adjacency matrix plays pivotal role; instead of the more common approach involving graph-Laplacian. In this work, we follow the adjacency matrix based approach and corresponding algebraic signal model. We further expand the theory and introduce the concept of similarity of two graphs. The similarity of graphs is useful in that key properties (such as filter-response, algebra related to graph) get transferred from one graph to another. We demonstrate potential applications of the relation between two similar graphs, such as nonuniform filter design, DTMF detection and signal reconstruction.

Keywords: graph signal processing, algebraic signal processing, graph similarity, isospectral graphs, nonuniform signal processing

Procedia PDF Downloads 316

Authors: Ming Su, Ziqiang Mu

Abstract:

This paper proposes a synthesis method for nonuniform linear antenna arrays that combine Gaussian process regression (GPR) and genetic algorithm (GA). In this method, the GPR model can be used to calculate the array radiation pattern in the presence of mutual coupling effects, and then the GA is used to optimize the excitations and locations of the elements so as to generate the desired radiation pattern. In this paper, taking a 9-element nonuniform linear array as an example and the desired radiation pattern corresponding to a Chebyshev distribution as the optimization objective, optimize the excitations and locations of the elements. Finally, the optimization results are verified by electromagnetic simulation software CST, which shows that the method is effective.

Keywords: nonuniform linear antenna arrays, GPR, GA, mutual coupling effects, active element pattern

Procedia PDF Downloads 80

Authors: Abdullah A. AlShaher

Abstract:

In this paper, we demonstrate how regression curves can be used to recognize 2D non-rigid handwritten shapes. Each shape is represented by a set of non-overlapping uniformly distributed landmarks. The underlying models utilize 2^nd order of polynomials to model shapes within a training set. To estimate the regression models, we need to extract the required coefficients which describe the variations for a set of shape class. Hence, a least square method is used to estimate such modes. We then proceed by training these coefficients using the apparatus Expectation Maximization algorithm. Recognition is carried out by finding the least error landmarks displacement with respect to the model curves. Handwritten isolated Arabic characters are used to evaluate our approach.

Keywords: character recognition, regression curves, handwritten Arabic letters, expectation maximization algorithm

Procedia PDF Downloads 113

Authors: Dahi Ghareab Abdelsalam Ibrahim

Abstract:

Calibration of step heights with high accuracy is needed for many applications in the industry. In general, step height consists of three bands: pass band, transition band (roll-off), and stop band. Abdelsalam used a convolution of the transfer functions of both Chebyshev type 2 and elliptic filters with WFF of the Fresnel transform in the frequency domain for producing a steeper roll-off with the removal of ripples in the pass band- and stop-bands. In this paper, we used a new method based on the Hamming window: band-pass filter for calibration of step heights in terms of perfect adjustment of pass-band, roll-off, and stop-band. The method is applied to calibrate a nominal step height of 40 cm. The step height is measured first by asynchronous dual-wavelength phase-shift interferometry. The measured step height is then calibrated by the simulation of the Hamming window: band-pass filter. The spectrum of the simulated band-pass filter is simulated at N = 881 and f0 = 0.24. We can conclude that the proposed method can calibrate any step height by adjusting only two factors which are N and f0.

Keywords: optical metrology, step heights, hamming window, band-pass filter

Procedia PDF Downloads 53

Authors: Debjani Chakraborty, Abhijit Chatterjee, Aishwaryaprajna

Abstract:

Posynomials, a special type of polynomials, having singularities, pose difficulties while solving geometric programming problems. In this paper, a methodology has been proposed and used to obtain extreme values for geometric programming problems by nth degree polynomial interpolation technique. Here the main idea to optimise the posynomial is to fit a best polynomial which has continuous gradient values throughout the range of the function. The approximating polynomial is smoothened to remove the discontinuities present in the feasible region and the objective function. This spatial interpolation method is capable to optimise univariate and multivariate geometric programming problems. An example is solved to explain the robustness of the methodology by considering a bivariate nonlinear geometric programming problem. This method is also applicable for signomial programming problem.

Keywords: geometric programming problem, multivariate optimisation technique, posynomial, spatial interpolation

Procedia PDF Downloads 328

Authors: Mohamed Othmani, Yassine Khlifi

Abstract:

This paper presents a technique for compact three dimensional (3D) object model reconstruction using wavelet networks. It consists to transform an input surface vertices into signals,and uses wavelet network parameters for signal approximations. To prove this, we use a wavelet network architecture founded on several mother wavelet families. POLYnomials WindOwed with Gaussians (POLYWOG) wavelet families are used to maximize the probability to select the best wavelets which ensure the good generalization of the network. To achieve a better reconstruction, the network is trained several iterations to optimize the wavelet network parameters until the error criterion is small enough. Experimental results will shown that our proposed technique can effectively reconstruct an irregular 3D object models when using the optimized wavelet network parameters. We will prove that an accurateness reconstruction depends on the best choice of the mother wavelets.

Keywords: 3d object, optimization, parametrization, polywog wavelets, reconstruction, wavelet networks

Procedia PDF Downloads 252

Authors: Tarul Garg, P. N. Agrawal

Abstract:

We propose to define the q-analogue of the α-Bernstein Kantorovich operators and then introduce the q-bivariate generalization of these operators to study the approximation of functions of two variables. We obtain the rate of convergence of these bivariate operators by means of the total modulus of continuity, partial modulus of continuity and the Peetre’s K-functional for continuous functions. Further, in order to study the approximation of functions of two variables in a space bigger than the space of continuous functions, i.e. Bögel space; the GBS (Generalized Boolean Sum) of the q-bivariate operators is considered and degree of approximation is discussed for the Bögel continuous and Bögel differentiable functions with the aid of the Lipschitz class and the mixed modulus of smoothness.

Keywords: Bögel continuous, Bögel differentiable, generalized Boolean sum, K-functional, mixed modulus of smoothness

Procedia PDF Downloads 350