Search results for: fixed point iteration
2377 Weak Convergence of Mann Iteration for a Hybrid Pair of Mappings in a Banach Space
Authors: Alemayehu Geremew Negash
Abstract:
We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E.
Keywords: Common fixed point, Mann iteration, Multivalued mapping, weak convergence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16272376 Convergence of a One-step Iteration Scheme for Quasi-asymptotically Nonexpansive Mappings
Authors: Safeer Hussain Khan
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In this paper, we use a one-step iteration scheme to approximate common fixed points of two quasi-asymptotically nonexpansive mappings. We prove weak and strong convergence theorems in a uniformly convex Banach space. Our results generalize the corresponding results of Yao and Chen [15] to a wider class of mappings while extend those of Khan, Abbas and Khan [4] to an improved one-step iteration scheme without any condition and improve upon many others in the literature.
Keywords: One-step iteration scheme, asymptotically quasi non expansive mapping, common fixed point, condition (a'), weak and strong convergence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14362375 Two-step Iterative Process For Common Fixed Points of Two Asymptotically Quasi-nonexpansive Mappings
Authors: Safeer Hussain Khan
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In this paper, we consider an iteration process for approximating common fixed points of two asymptotically quasinonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces.Keywords: Asypmtotically quasi-nonexpansive mappings, Commonfixed point, Strong and weak convergence, Iteration process.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15262374 Simulation Tools for Fixed Point DSP Algorithms and Architectures
Authors: K. B. Cullen, G. C. M. Silvestre, N. J. Hurley
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This paper presents software tools that convert the C/Cµ floating point source code for a DSP algorithm into a fixedpoint simulation model that can be used to evaluate the numericalperformance of the algorithm on several different fixed pointplatforms including microprocessors, DSPs and FPGAs. The tools use a novel system for maintaining binary point informationso that the conversion from floating point to fixed point isautomated and the resulting fixed point algorithm achieves maximum possible precision. A configurable architecture is used during the simulation phase so that the algorithm can produce a bit-exact output for several different target devices.
Keywords: DSP devices, DSP algorithm, simulation model, software
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 25372373 A Reconfigurable Processing Element for Cholesky Decomposition and Matrix Inversion
Authors: Aki Happonen, Adrian Burian, Erwin Hemming
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Fixed-point simulation results are used for the performance measure of inverting matrices by Cholesky decomposition. The fixed-point Cholesky decomposition algorithm is implemented using a fixed-point reconfigurable processing element. The reconfigurable processing element provides all mathematical operations required by Cholesky decomposition. The fixed-point word length analysis is based on simulations using different condition numbers and different matrix sizes. Simulation results show that 16 bits word length gives sufficient performance for small matrices with low condition number. Larger matrices and higher condition numbers require more dynamic range for a fixedpoint implementation.Keywords: Cholesky Decomposition, Fixed-point, Matrix inversion, Reconfigurable processing.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16802372 Fixed Point of Lipschitz Quasi Nonexpansive Mappings
Authors: M. Moosavi, H. Khatibzadeh
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In this article, we study demiclosed and strongly quasi-nonexpansive of a sequence generated by the proximal point algorithm for a finite family of quasi-nonexpansive mappings in Hadamard spaces. Δ-convergence of iterations for the sequence of strongly quasi-nonexpansive mappings as well as the strong convergence of the Halpern type regularization of them to a common fixed point of sequence are also established. Our results generalize and improve several previously known results of the existing literature.
Keywords: Fixed point, Hadamard space, proximal point algorithm, quasi-nonexpansive sequence of mappings, resolvent.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1632371 A Reconfigurable Processing Element Implementation for Matrix Inversion Using Cholesky Decomposition
Authors: Aki Happonen, Adrian Burian, Erwin Hemming
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Fixed-point simulation results are used for the performance measure of inverting matrices using a reconfigurable processing element. Matrices are inverted using the Cholesky decomposition algorithm. The reconfigurable processing element is capable of all required mathematical operations. The fixed-point word length analysis is based on simulations of different condition numbers and different matrix sizes.Keywords: Cholesky Decomposition, Fixed-point, Matrixinversion, Reconfigurable processing.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16142370 A Constructive Proof of the General Brouwer Fixed Point Theorem and Related Computational Results in General Non-Convex sets
Authors: Menglong Su, Shaoyun Shi, Qing Xu
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In this paper, by introducing twice continuously differentiable mappings, we develop an interior path following following method, which enables us to give a constructive proof of the general Brouwer fixed point theorem and thus to solve fixed point problems in a class of non-convex sets. Under suitable conditions, a smooth path can be proven to exist. This can lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper.
Keywords: interior path following method, general Brouwer fixed point theorem, non-convex sets, globally convergent algorithm
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14352369 Common Fixed Point Theorems for Co-Cyclic Weak Contractions in Compact Metric
Authors: Alemayehu Geremew Negash
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In this paper, we prove some common fixed point theorems for co-cyclic weak contractions in compact metric spaces.
Keywords: Cyclic weak contraction, Co-cyclic weak contraction, Co-cyclic representation, Common fixed point.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21972368 Iteration Acceleration for Nonlinear Coupled Parabolic-Hyperbolic System
Authors: Xia Cui, Guang-wei Yuan, Jing-yan Yue
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A Picard-Newton iteration method is studied to accelerate the numerical solution procedure of a class of two-dimensional nonlinear coupled parabolic-hyperbolic system. The Picard-Newton iteration is designed by adding higher-order terms of small quantity to an existing Picard iteration. The discrete functional analysis and inductive hypothesis reasoning techniques are used to overcome difficulties coming from nonlinearity and coupling, and theoretical analysis is made for the convergence and approximation properties of the iteration scheme. The Picard-Newton iteration has a quadratic convergent ratio, and its solution has second order spatial approximation and first order temporal approximation to the exact solution of the original problem. Numerical tests verify the results of the theoretical analysis, and show the Picard-Newton iteration is more efficient than the Picard iteration.
Keywords: Nonlinearity, iterative acceleration, coupled parabolic hyperbolic system, quadratic convergence, numerical analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15492367 Ordinary Differential Equations with Inverted Functions
Authors: Thomas Kampke
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Equations with differentials relating to the inverse of an unknown function rather than to the unknown function itself are solved exactly for some special cases and numerically for the general case. Invertibility combined with differentiability over connected domains forces solutions always to be monotone. Numerical function inversion is key to all solution algorithms which either are of a forward type or a fixed point type considering whole approximate solution functions in each iteration. The given considerations are restricted to ordinary differential equations with inverted functions (ODEIs) of first order. Forward type computations, if applicable, admit consistency of order one and, under an additional accuracy condition, convergence of order one.
Keywords: Euler method, fixed points, golden section, multi-step procedures, Runge Kutta methods.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14342366 Error Propagation of the Hidden-Point Bar Method: Effect of Bar Geometry
Authors: Said M. Easa, Ahmed Shaker
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The hidden-point bar method is useful in many surveying applications. The method involves determining the coordinates of a hidden point as a function of horizontal and vertical angles measured to three fixed points on the bar. Using these measurements, the procedure involves calculating the slant angles, the distances from the station to the fixed points, the coordinates of the fixed points, and then the coordinates of the hidden point. The propagation of the measurement errors in this complex process has not been fully investigated in the literature. This paper evaluates the effect of the bar geometry on the position accuracy of the hidden point which depends on the measurement errors of the horizontal and vertical angles. The results are used to establish some guidelines regarding the inclination angle of the bar and the location of the observed points that provide the best accuracy.Keywords: Hidden point, accuracy, error propagation, surveying, evaluation, simulation, geometry.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17082365 The Positive Solution for Singular Eigenvalue Problem of One-dimensional p-Laplace Operator
Authors: Lv Yuhua
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In this paper, by constructing a special cone and using fixed point theorem and fixed point index theorem of cone, we get the existence of positive solution for a class of singular eigenvalue value problems with p-Laplace operator, which improved and generalized the result of related paper.
Keywords: Cone, fixed point index, eigenvalue problem, p-Laplace operator, positive solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14192364 Power Series Form for Solving Linear Fredholm Integral Equations of Second Order via Banach Fixed Point Theorem
Authors: Adil AL-Rammahi
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In this paper, a new method for solution of second order linear Fredholm integral equation in power series form was studied. The result is obtained by using Banach fixed point theorem.
Keywords: Fredholm integral equation, power series, Banach fixed point theorem, Linear Systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 24772363 Constructive Proof of Tychonoff’s Fixed Point Theorem for Sequentially Locally Non-Constant Functions
Authors: Yasuhito Tanaka
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We present a constructive proof of Tychonoff’s fixed point theorem in a locally convex space for uniformly continuous and sequentially locally non-constant functions.
Keywords: sequentially locally non-constant functions, Tychonoff’s fixed point theorem, constructive mathematics.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14932362 Fixed Point Theorems for Set Valued Mappings in Partially Ordered Metric Spaces
Authors: Ismat Beg, Asma Rashid Butt
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Let (X,) be a partially ordered set and d be a metric on X such that (X, d) is a complete metric space. Assume that X satisfies; if a non-decreasing sequence xn → x in X, then xn x, for all n. Let F be a set valued mapping from X into X with nonempty closed bounded values satisfying; (i) there exists κ ∈ (0, 1) with D(F(x), F(y)) ≤ κd(x, y), for all x y, (ii) if d(x, y) < ε < 1 for some y ∈ F(x) then x y, (iii) there exists x0 ∈ X, and some x1 ∈ F(x0) with x0 x1 such that d(x0, x1) < 1. It is shown that F has a fixed point. Several consequences are also obtained.
Keywords: Fixed point, partially ordered set, metric space, set valued mapping.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20242361 Algorithms for Computing of Optimization Problems with a Common Minimum-Norm Fixed Point with Applications
Authors: Apirak Sombat, Teerapol Saleewong, Poom Kumam, Parin Chaipunya, Wiyada Kumam, Anantachai Padcharoen, Yeol Je Cho, Thana Sutthibutpong
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This research is aimed to study a two-step iteration process defined over a finite family of σ-asymptotically quasi-nonexpansive nonself-mappings. The strong convergence is guaranteed under the framework of Banach spaces with some additional structural properties including strict and uniform convexity, reflexivity, and smoothness assumptions. With similar projection technique for nonself-mapping in Hilbert spaces, we hereby use the generalized projection to construct a point within the corresponding domain. Moreover, we have to introduce the use of duality mapping and its inverse to overcome the unavailability of duality representation that is exploit by Hilbert space theorists. We then apply our results for σ-asymptotically quasi-nonexpansive nonself-mappings to solve for ideal efficiency of vector optimization problems composed of finitely many objective functions. We also showed that the obtained solution from our process is the closest to the origin. Moreover, we also give an illustrative numerical example to support our results.Keywords: σ-asymptotically quasi-nonexpansive nonselfmapping, strong convergence, fixed point, uniformly convex and uniformly smooth Banach space.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 10892360 Neural Network in Fixed Time for Collision Detection between Two Convex Polyhedra
Authors: M. Khouil, N. Saber, M. Mestari
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In this paper, a different architecture of a collision detection neural network (DCNN) is developed. This network, which has been particularly reviewed, has enabled us to solve with a new approach the problem of collision detection between two convex polyhedra in a fixed time (O (1) time). We used two types of neurons, linear and threshold logic, which simplified the actual implementation of all the networks proposed. The study of the collision detection is divided into two sections, the collision between a point and a polyhedron and then the collision between two convex polyhedra. The aim of this research is to determine through the AMAXNET network a mini maximum point in a fixed time, which allows us to detect the presence of a potential collision.
Keywords: Collision identification, fixed time, convex polyhedra, neural network, AMAXNET.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18062359 Variational Iteration Method for the Solution of Boundary Value Problems
Authors: Olayiwola M.O., Gbolagade A .W., Akinpelu F. O.
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In this work, we present a reliable framework to solve boundary value problems with particular significance in solid mechanics. These problems are used as mathematical models in deformation of beams. The algorithm rests mainly on a relatively new technique, the Variational Iteration Method. Some examples are given to confirm the efficiency and the accuracy of the method.
Keywords: Variational iteration method, boundary value problems, convergence, restricted variation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20892358 Positive Solutions for Three-Point Boundary Value Problems of Third-Order Nonlinear Singular Differential Equations in Banach Space
Authors: Li Xiguang
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In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for singular differential equation in Banach space, which improved and generalize the result of related paper.
Keywords: Banach space, cone, fixed point index, singular differential equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14572357 Existence of Solution for Singular Two-point Boundary Value Problem of Second-order Differential Equation
Authors: Xiguang Li
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In this paper, by constructing a special set and utilizing fixed point theory in coin, we study the existence of solution of singular two point’s boundary value problem for second-order differential equation, which improved and generalize the result of related paper.
Keywords: Singular differential equation, boundary value problem, coin, fixed point theory.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11182356 Numerical Analysis of Electrical Interaction between two Axisymmetric Spheroids
Authors: Kuan-Liang Liu, Eric Lee, Jung-Jyh Lee, Jyh-Ping Hsu
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The electrical interaction between two axisymmetric spheroidal particles in an electrolyte solution is examined numerically. A Galerkin finite element method combined with a Newton-Raphson iteration scheme is proposed to evaluate the spatial variation in the electrical potential, and the result obtained used to estimate the interaction energy between two particles. We show that if the surface charge density is fixed, the potential gradient is larger at a point, which has a larger curvature, and if surface potential is fixed, surface charge density is proportional to the curvature. Also, if the total interaction energy against closest surface-to-surface curve exhibits a primary maximum, the maximum follows the order (oblate-oblate) > (sphere-sphere)>(oblate-prolate)>(prolate-prolate), and if the curve has a secondary minimum, the absolute value of the minimum follows the same order.Keywords: interaction energy, interaction force, Poisson-Boltzmann equation, spheroid.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14602355 MEGSOR Iterative Scheme for the Solution of 2D Elliptic PDE's
Authors: J. Sulaiman, M. Othman, M. K. Hasan
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Recently, the findings on the MEG iterative scheme has demonstrated to accelerate the convergence rate in solving any system of linear equations generated by using approximation equations of boundary value problems. Based on the same scheme, the aim of this paper is to investigate the capability of a family of four-point block iterative methods with a weighted parameter, ω such as the 4 Point-EGSOR, 4 Point-EDGSOR, and 4 Point-MEGSOR in solving two-dimensional elliptic partial differential equations by using the second-order finite difference approximation. In fact, the formulation and implementation of three four-point block iterative methods are also presented. Finally, the experimental results show that the Four Point MEGSOR iterative scheme is superior as compared with the existing four point block schemes.
Keywords: MEG iteration, second-order finite difference, weighted parameter.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16952354 Positive Solutions of Second-order Singular Differential Equations in Banach Space
Authors: Li Xiguang
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In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for the boundary value problem of second-order singular differential equations in Banach space, which improved and generalize the result of related paper.
Keywords: Banach space, cone, fixed point index, singular equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12352353 Some Third Order Methods for Solving Systems of Nonlinear Equations
Authors: Janak Raj Sharma, Rajni Sharma
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Based on Traub-s methods for solving nonlinear equation f(x) = 0, we develop two families of third-order methods for solving system of nonlinear equations F(x) = 0. The families include well-known existing methods as special cases. The stability is corroborated by numerical results. Comparison with well-known methods shows that the present methods are robust. These higher order methods may be very useful in the numerical applications requiring high precision in their computations because these methods yield a clear reduction in number of iterations.Keywords: Nonlinear equations and systems, Newton's method, fixed point iteration, order of convergence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21932352 Positive Solutions for Systems of Nonlinear Third-Order Differential Equations with p-Laplacian
Authors: Li Xiguang
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In this paper, by constructing a special set and utilizing fixed point theory, we study the existence and multiplicity of the positive solutions for systems of nonlinear third-order differential equations with p-laplacian, which improve and generalize the result of related paper.Keywords: p-Laplacian, cone, fixed point theorem, positive solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5822351 Two Fourth-order Iterative Methods Based on Continued Fraction for Root-finding Problems
Authors: Shengfeng Li, Rujing Wang
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In this paper, we present two new one-step iterative methods based on Thiele-s continued fraction for solving nonlinear equations. By applying the truncated Thiele-s continued fraction twice, the iterative methods are obtained respectively. Analysis of convergence shows that the new methods are fourth-order convergent. Numerical tests verifying the theory are given and based on the methods, two new one-step iterations are developed.Keywords: Iterative method, Fixed-point iteration, Thiele's continued fraction, Order of convergence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18692350 On Tarski’s Type Theorems for L-Fuzzy Isotone and L-Fuzzy Relatively Isotone Maps on L-Complete Propelattices
Authors: František Včelař, Zuzana Pátíková
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Recently a new type of very general relational structures, the so called (L-)complete propelattices, was introduced. These significantly generalize complete lattices and completely lattice L-ordered sets, because they do not assume the technically very strong property of transitivity. For these structures also the main part of the original Tarski’s fixed point theorem holds for (L-fuzzy) isotone maps, i.e., the part which concerns the existence of fixed points and the structure of their set. In this paper, fundamental properties of (L-)complete propelattices are recalled and the so called L-fuzzy relatively isotone maps are introduced. For these maps it is proved that they also have fixed points in L-complete propelattices, even if their set does not have to be of an awaited analogous structure of a complete propelattice.Keywords: Fixed point, L-complete propelattice, L-fuzzy (relatively) isotone map, residuated lattice, transitivity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 11032349 The Symmetric Solutions for Three-Point Singular Boundary Value Problems of Differential Equation
Authors: Li Xiguang
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In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.
Keywords: Banach space, cone, fixed point index, singular differential equation, p-Laplace operator, symmetric solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14012348 Existence of Positive Solutions for Second-Order Difference Equation with Discrete Boundary Value Problem
Authors: Thanin Sitthiwirattham, Jiraporn Reunsumrit
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We study the existence of positive solutions to the three points difference-summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.
Keywords: Positive solution, Boundary value problem, Fixed point theorem, Cone.
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