**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1837

# Search results for: Approximation Theory

##### 1837 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.

##### 1836 Some Separations in Covering Approximation Spaces

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

**Abstract:**

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

##### 1835 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.

##### 1834 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.

##### 1833 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.

##### 1832 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

##### 1831 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.

##### 1830 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.

##### 1829 Generalization Kernel for Geopotential Approximation by Harmonic Splines

**Authors:**
Elena Kotevska

**Abstract:**

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

##### 1828 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.

##### 1827 Design of Two-Channel Quadrature Mirror Filter Banks Using Digital All-Pass Filters

**Authors:**
Ju-Hong Lee,
Yi-Lin Shieh

**Abstract:**

The paper deals with the minimax design of two-channel linear-phase (LP) quadrature mirror filter (QMF) banks using infinite impulse response (IIR) digital all-pass filters (DAFs). Based on the theory of two-channel QMF banks using two IIR DAFs, the design problem is appropriately formulated to result in an appropriate Chebyshev approximation for the desired group delay responses of the IIR DAFs and the magnitude response of the low-pass analysis filter. Through a frequency sampling and iterative approximation method, the design problem can be solved by utilizing a weighted least squares approach. The resulting two-channel QMF banks can possess approximately LP response without magnitude distortion. Simulation results are presented for illustration and comparison.

**Keywords:**
Chebyshev approximation,
Digital All-Pass Filter,
Quadrature Mirror Filter,
Weighted Least Squares.

##### 1826 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.

##### 1825 Adaptive Impedance Control for Unknown Time-Varying Environment Position and Stiffness

**Authors:**
Norsinnira Zainul Azlan,
Hiroshi Yamaura

**Abstract:**

This study is concerned with a new adaptive impedance control strategy to compensate for unknown time-varying environment stiffness and position. The uncertainties are expressed by Function Approximation Technique (FAT), which allows the update laws to be derived easily using Lyapunov stability theory. Computer simulation results are presented to validate the effectiveness of the proposed strategy.

**Keywords:**
Adaptive Impedance Control,
Function Approximation Technique (FAT),
unknown time-varying environment position and stiffness.

##### 1824 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.

##### 1823 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.

##### 1822 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.

##### 1821 Theoretical Calculation of Electrical and Optical Properties of BaZrO3

**Authors:**
Leyla Safaie Kouchaksaraie

**Abstract:**

**Keywords:**
Density Functional Theory (DFT),
Full PotentialLinearized Augmented Plane Wave (Fp-LAPW),
GeneralizedGradient Approximation (GGA),
Linearized Augmented Plane Wave(LAPW),
Local Density Approximation (LDA)

##### 1820 Application of Granular Computing Paradigm in Knowledge Induction

**Authors:**
Iftikhar U. Sikder

**Abstract:**

This paper illustrates an application of granular computing approach, namely rough set theory in data mining. The paper outlines the formalism of granular computing and elucidates the mathematical underpinning of rough set theory, which has been widely used by the data mining and the machine learning community. A real-world application is illustrated, and the classification performance is compared with other contending machine learning algorithms. The predictive performance of the rough set rule induction model shows comparative success with respect to other contending algorithms.

**Keywords:**
Concept approximation,
granular computing,
reducts,
rough set theory,
rule induction.

##### 1819 On Diffusion Approximation of Discrete Markov Dynamical Systems

**Authors:**
Jevgenijs Carkovs

**Abstract:**

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

##### 1818 Adaptive Impedance Control for Unknown Non-Flat Environment

**Authors:**
Norsinnira Zainul Azlan,
Hiroshi Yamaura

**Abstract:**

**Keywords:**
Adaptive impedance control,
Function
Approximation Technique (FAT),
impedance control,
unknown
environment position.

##### 1817 Synthesis of Wavelet Filters using Wavelet Neural Networks

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

**Abstract:**

**Keywords:**
Beta wavelets,
Wavenet,
multiresolution analysis,
perfect filter reconstruction,
salient point detect,
repeatability.

##### 1816 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

##### 1815 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.

##### 1814 Study of Structural and Electronic Properties of Ternary PdMnGe Half-Heusler Alloy

**Authors:**
F. Bendahma,
M. Mana,
B. Bestani,
S. Bentata

**Abstract:**

This study deals with the structural and electronic properties of ternary PdMnGe Half-Heusler alloy using the full potential linearized augmented plane wave (FP-LAPW) method based on the density functional theory (DFT) as implemented in the WIEN2k package, within the framework of generalized gradient approximation (GGA). Structural parameters, total and partial densities of states were also analyzed. The obtained result shows that the studied material is metallic in GGA treatment. The elastic constants (*Cij*) show that our compound is ductile, stiff and anisotropic.

**Keywords:**
Full potential linearized augmented plane wave,
generalized gradient approximation treatment,
Half-Heusler,
structural and electronic properties.

##### 1813 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

##### 1812 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.

##### 1811 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.

##### 1810 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.

##### 1809 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.

##### 1808 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.