**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**398

# Search results for: Approximation

##### 398 Best Co-approximation and Best Simultaneous Co-approximation in Fuzzy Normed Spaces

**Authors:**
J. Kavikumar,
N. S. Manian,
M.B.K. Moorthy

**Abstract:**

The main purpose of this paper is to consider the t-best co-approximation and t-best simultaneous co-approximation in fuzzy normed spaces. We develop the theory of t-best co-approximation and t-best simultaneous co-approximation in quotient spaces. This new concept is employed us to improve various characterisations of t-co-proximinal and t-co-Chebyshev sets.

**Keywords:**
Fuzzy best co-approximation,
fuzzy quotient spaces,
proximinality,
Chebyshevity,
best simultaneous co-approximation.

##### 397 Definable Subsets in Covering Approximation Spaces

**Authors:**
Xun Ge,
Zhaowen Li

**Abstract:**

**Keywords:**
Covering approximation space,
covering approximation operator,
definable subset,
inner definable subset,
outer definable subset.

##### 396 On an Open Problem for Definable Subsets of Covering Approximation Spaces

**Authors:**
Mei He,
Ying Ge,
Jingyu Qian

**Abstract:**

**Keywords:**
Covering approximation space,
covering approximation operator,
definable subset,
inner definable subset,
outer definable subset.

##### 395 Comparison between Beta Wavelets Neural Networks, RBF Neural Networks and Polynomial Approximation for 1D, 2DFunctions Approximation

**Authors:**
Wajdi Bellil,
Chokri Ben Amar,
Adel M. Alimi

**Abstract:**

This paper proposes a comparison between wavelet neural networks (WNN), RBF neural network and polynomial approximation in term of 1-D and 2-D functions approximation. We present a novel wavelet neural network, based on Beta wavelets, for 1-D and 2-D functions approximation. Our purpose is to approximate an unknown function f: Rn - R from scattered samples (xi; y = f(xi)) i=1....n, where first, we have little a priori knowledge on the unknown function f: it lives in some infinite dimensional smooth function space and second the function approximation process is performed iteratively: each new measure on the function (xi; f(xi)) is used to compute a new estimate Ôêºf as an approximation of the function f. Simulation results are demonstrated to validate the generalization ability and efficiency of the proposed Beta wavelet network.

**Keywords:**
Beta wavelets networks,
RBF neural network,
training algorithms,
MSE,
1-D,
2D function approximation.

##### 394 Some Separations in Covering Approximation Spaces

**Authors:**
Xun Ge,
Jinjin Li,
Ying Ge

**Abstract:**

**Keywords:**
Rough set,
covering approximation space,
granularitywise separation.

##### 393 An Empirical Validation of the Linear- Hyperbolic Approximation of the I-V Characteristic of a Solar Cell Generator

**Authors:**
A. A. Penin

**Abstract:**

An empirical linearly-hyperbolic approximation of the I - V characteristic of a solar cell is presented. This approximation is based on hyperbolic dependence of a current of p-n junctions on voltage for large currents. Such empirical approximation is compared with the early proposed formal linearly-hyperbolic approximation of a solar cell. The expressions defining laws of change of parameters of formal approximation at change of a photo current of family of characteristics are received. It allows simplifying a finding of parameters of approximation on actual curves, to specify their values. Analytical calculation of load regime for linearly - hyperbolic model leads to quadratic equation. Also, this model allows to define soundly a deviation from the maximum power regime and to compare efficiency of regimes of solar cells with different parameters.

**Keywords:**
a solar cell generator,
I − V characteristic,
p − n junction,
approximation

##### 392 Constant Factor Approximation Algorithm for p-Median Network Design Problem with Multiple Cable Types

**Authors:**
Chaghoub Soraya,
Zhang Xiaoyan

**Abstract:**

**Keywords:**
Approximation algorithms,
buy-at-bulk,
combinatorial
optimization,
network design,
p-median.

##### 391 Approximation to the Hardy Operator on Topological Measure Spaces

**Authors:**
Kairat T. Mynbaev,
Elena N. Lomakina

**Abstract:**

We consider a Hardy type operator generated by a family of open subsets of a Hausdorff topological space. The family is indexed with non-negative real numbers and is totally ordered. For this operator, we obtain two-sided bounds of its norm, a compactness criterion and bounds for its approximation numbers. Previously bounds for its approximation numbers have been established only in the one-dimensional case, while we do not impose any restrictions on the dimension of the Hausdorff space. The bounds for the norm and conditions for compactness have been found earlier but our approach is different in that we use domain partitions for all problems under consideration.

**Keywords:**
Approximation numbers,
boundedness and
compactness,
multidimensional Hardy operator,
Hausdorff
topological space.

##### 390 Denoising and Compression in Wavelet Domainvia Projection on to Approximation Coefficients

**Authors:**
Mario Mastriani

**Abstract:**

We describe a new filtering approach in the wavelet domain for image denoising and compression, based on the projections of details subbands coefficients (resultants of the splitting procedure, typical in wavelet domain) onto the approximation subband coefficients (much less noisy). The new algorithm is called Projection Onto Approximation Coefficients (POAC). As a result of this approach, only the approximation subband coefficients and three scalars are stored and/or transmitted to the channel. Besides, with the elimination of the details subbands coefficients, we obtain a bigger compression rate. Experimental results demonstrate that our approach compares favorably to more typical methods of denoising and compression in wavelet domain.

**Keywords:**
Compression,
denoising,
projections,
wavelets.

##### 389 A Note on Negative Hypergeometric Distribution and Its Approximation

**Authors:**
S. B. Mansuri

**Abstract:**

**Keywords:**
Negative hypergeometric distribution,
Poisson distribution,
Poisson approximation,
Stein-Chen identity,
w-function.

##### 388 The Inverse Problem of Nonsymmetric Matrices with a Submatrix Constraint and its Approximation

**Authors:**
Yongxin Yuan,
Hao Liu

**Abstract:**

In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given matrices X ∈ Rn×p, B ∈ Rp×p and A0 ∈ Rr×r, find a matrix A ∈ Rn×n such that XT AX − B = min, s. t. A([1, r]) = A0, where A([1, r]) is the r×r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n × n matrix A˜ with A˜([1, r]) = A0, find Aˆ ∈ SE such that A˜ − Aˆ = minA∈SE A˜ − A, where SE is the solution set of LSP. We show that the best approximation solution Aˆ is unique and derive an explicit formula for it. Keyw

**Keywords:**
Inverse problem,
Least-squares solution,
model updating,
Singular value decomposition (SVD),
Optimal approximation.

##### 387 Approximation Algorithm for the Shortest Approximate Common Superstring Problem

**Authors:**
A.S. Rebaï,
M. Elloumi

**Abstract:**

**Keywords:**
Shortest approximate common superstring,
approximation algorithms,
strings overlaps,
complexities.

##### 386 Properties and Approximation Distribution Reductions in Multigranulation Rough Set Model

**Authors:**
Properties,
Approximation Distribution Reductions in Multigranulation Rough Set Model

**Abstract:**

Some properties of approximation sets are studied in multi-granulation optimist model in rough set theory using maximal compatible classes. The relationships between or among lower and upper approximations in single and multiple granulation are compared and discussed. Through designing Boolean functions and discernibility matrices in incomplete information systems, the lower and upper approximation sets and reduction in multi-granulation environments can be found. By using examples, the correctness of computation approach is consolidated. The related conclusions obtained are suitable for further investigating in multiple granulation RSM.

**Keywords:**
Incomplete information system,
maximal compatible class,
multi-granulation rough set model,
reduction.

##### 385 On Diffusion Approximation of Discrete Markov Dynamical Systems

**Authors:**
Jevgenijs Carkovs

**Abstract:**

**Keywords:**
Markov dynamical system,
diffusion approximation,
equilibrium stochastic stability.

##### 384 Implemented 5-bit 125-MS/s Successive Approximation Register ADC on FPGA

**Authors:**
S. Heydarzadeh,
A. Kadivarian,
P. Torkzadeh

**Abstract:**

**Keywords:**
Analog to digital converter,
Successive
approximation,
Capacitor switching algorithm,
FPGA

##### 383 Reduction of Linear Time-Invariant Systems Using Routh-Approximation and PSO

**Authors:**
S. Panda,
S. K. Tomar,
R. Prasad,
C. Ardil

**Abstract:**

Order reduction of linear-time invariant systems employing two methods; one using the advantages of Routh approximation and other by an evolutionary technique is presented in this paper. In Routh approximation method the denominator of the reduced order model is obtained using Routh approximation while the numerator of the reduced order model is determined using the indirect approach of retaining the time moments and/or Markov parameters of original system. By this method the reduced order model guarantees stability if the original high order model is stable. In the second method Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical examples.

**Keywords:**
Model Order Reduction,
Markov Parameters,
Routh Approximation,
Particle Swarm Optimization,
Integral Squared Error,
Steady State Stability.

##### 382 Approximation for Average Error Probability of BPSK in the Presence of Phase Error

**Authors:**
Yeonsoo Jang,
Dongweon Yoon,
Ki Ho Kwon,
Jaeyoon Lee,
Wooju Lee

**Abstract:**

**Keywords:**
Average error probability,
Phase shift keying,
Phase
error

##### 381 A Study on the Least Squares Reduced Parameter Approximation of FIR Digital Filters

**Authors:**
S. Seyedtabaii,
E. Seyedtabaii

**Abstract:**

**Keywords:**
Digital filter,
filter approximation,
least squares,
model order reduction.

##### 380 Particle Swarm Optimization and Quantum Particle Swarm Optimization to Multidimensional Function Approximation

**Authors:**
Diogo Silva,
Fadul Rodor,
Carlos Moraes

**Abstract:**

**Keywords:**
PSO,
QPSO,
function approximation,
AI,
optimization,
multidimensional functions.

##### 379 Localising Gauss's Law and the Electric Charge Induction on a Conducting Sphere

**Authors:**
Sirapat Lookrak,
Anol Paisal

**Abstract:**

Space debris has numerous manifestations including ferro-metalize and non-ferrous. The electric field will induce negative charges to split from positive charges inside the space debris. In this research, we focus only on conducting materials. The assumption is that the electric charge density of a conducting surface is proportional to the electric field on that surface due to Gauss's law. We are trying to find the induced charge density from an external electric field perpendicular to a conducting spherical surface. An object is a sphere on which the external electric field is not uniform. The electric field is, therefore, considered locally. The localised spherical surface is a tangent plane so the Gaussian surface is a very small cylinder and every point on a spherical surface has its own cylinder. The electric field from a circular electrode has been calculated in near-field and far-field approximation and shown Explanation Touchless manoeuvring space debris orbit properties. The electric charge density calculation from a near-field and far-field approximation is done.

**Keywords:**
Near-field approximation,
far-field approximation,
localized Gauss’s law,
electric charge density.

##### 378 The Profit Trend of Cosmetics Products Using Bootstrap Edgeworth Approximation

**Authors:**
Edlira Donefski,
Lorenc Ekonomi,
Tina Donefski

**Abstract:**

**Keywords:**
Bootstrap,
Edgeworth approximation,
independent and Identical distributed,
quantile.

##### 377 Multiresolution Approach to Subpixel Registration by Linear Approximation of PSF

**Authors:**
Erol Seke,
Kemal Özkan

**Abstract:**

Linear approximation of point spread function (PSF) is a new method for determining subpixel translations between images. The problem with the actual algorithm is the inability of determining translations larger than 1 pixel. In this paper a multiresolution technique is proposed to deal with the problem. Its performance is evaluated by comparison with two other well known registration method. In the proposed technique the images are downsampled in order to have a wider view. Progressively decreasing the downsampling rate up to the initial resolution and using linear approximation technique at each step, the algorithm is able to determine translations of several pixels in subpixel levels.

**Keywords:**
Point Spread Function,
Subpixel translation,
Superresolution,
Multiresolution approach.

##### 376 Design of Stable IIR Digital Filters with Specified Group Delay Errors

**Authors:**
Yasunori Sugita,
Toshinori Yoshikawa

**Abstract:**

**Keywords:**
Filter design,
Group delay approximation,
Stable IIRfilters,
Successive projection method.

##### 375 A New Approach to Solve Blasius Equation using Parameter Identification of Nonlinear Functions based on the Bees Algorithm (BA)

**Authors:**
E. Assareh,
M.A. Behrang,
M. Ghalambaz,
A.R. Noghrehabadi,
A. Ghanbarzadeh

**Abstract:**

**Keywords:**
Bees Algorithm (BA); Approximate Solutions;
Blasius Differential Equation.

##### 374 Generalization Kernel for Geopotential Approximation by Harmonic Splines

**Authors:**
Elena Kotevska

**Abstract:**

**Keywords:**
Geopotential,
Reproducing Kernel,
Approximation,
Regular Surface

##### 373 The Error Analysis of An Upwind Difference Approximation for a Singularly Perturbed Problem

**Authors:**
Jiming Yang

**Abstract:**

An upwind difference approximation is used for a singularly perturbed problem in material science. Based on the discrete Green-s function theory, the error estimate in maximum norm is achieved, which is first-order uniformly convergent with respect to the perturbation parameter. The numerical experimental result is verified the valid of the theoretical analysis.

**Keywords:**
Singularly perturbed,
upwind difference,
uniform convergence.

##### 372 A New Method for Contour Approximation Using Basic Ramer Idea

**Authors:**
Ali Abdrhman Ukasha

**Abstract:**

**Keywords:**
Polygonal approximation,
Ramer,
Triangle and
Trapezoid methods.

##### 371 Function Approximation with Radial Basis Function Neural Networks via FIR Filter

**Authors:**
Kyu Chul Lee,
Sung Hyun Yoo,
Choon Ki Ahn,
Myo Taeg Lim

**Abstract:**

Recent experimental evidences have shown that because of a fast convergence and a nice accuracy, neural networks training via extended kalman filter (EKF) method is widely applied. However, as to an uncertainty of the system dynamics or modeling error, the performance of the method is unreliable. In order to overcome this problem in this paper, a new finite impulse response (FIR) filter based learning algorithm is proposed to train radial basis function neural networks (RBFN) for nonlinear function approximation. Compared to the EKF training method, the proposed FIR filter training method is more robust to those environmental conditions. Furthermore , the number of centers will be considered since it affects the performance of approximation.

**Keywords:**
Extended kalmin filter (EKF),
classification problem,
radial basis function networks (RBFN),
finite impulse response (FIR)filter.

##### 370 RANFIS : Rough Adaptive Neuro-Fuzzy Inference System

**Authors:**
Sandeep Chandana,
Rene V. Mayorga

**Abstract:**

The paper presents a new hybridization methodology involving Neural, Fuzzy and Rough Computing. A Rough Sets based approximation technique has been proposed based on a certain Neuro – Fuzzy architecture. A New Rough Neuron composition consisting of a combination of a Lower Bound neuron and a Boundary neuron has also been described. The conventional convergence of error in back propagation has been given away for a new framework based on 'Output Excitation Factor' and an inverse input transfer function. The paper also presents a brief comparison of performances, of the existing Rough Neural Networks and ANFIS architecture against the proposed methodology. It can be observed that the rough approximation based neuro-fuzzy architecture is superior to its counterparts.

**Keywords:**
Boundary neuron,
neuro-fuzzy,
output excitation factor,
RANFIS,
rough approximation,
rough neural computing.

##### 369 A Model to Study the Effect of Na+ ions on Ca2+diffusion under Rapid Buffering Approximation

**Authors:**
Vikas Tewari,
K.R. Pardasani

**Abstract:**

**Keywords:**
rapid buffer approximation,
sodium-calcium exchangeprotein,
Sarcolemmal Calcium ATPase pump,
buffer disassociationrate,
forward time centred space.