**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**5162

# Search results for: second order polynomial

##### 5162 Factoring a Polynomial with Multiple-Roots

**Authors:**
Feng Cheng Chang

**Abstract:**

**Keywords:**
Polynomial roots,
greatest common divisor,
Longhand polynomial division,
Euclidean GCD Algorithm.

##### 5161 A New Approach to Polynomial Neural Networks based on Genetic Algorithm

**Authors:**
S. Farzi

**Abstract:**

**Keywords:**
GMDH,
GPNN,
GA,
PNN.

##### 5160 Transformations between Bivariate Polynomial Bases

**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 e.t.c.. The aim of this short note 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.

##### 5159 Non-Polynomial Spline Solution of Fourth-Order Obstacle Boundary-Value Problems

**Authors:**
Jalil Rashidinia,
Reza Jalilian

**Abstract:**

**Keywords:**
Quintic non-polynomial spline,
Boundary formula,
Convergence,
Obstacle problems.

##### 5158 Stress Solitary Waves Generated by a Second-Order Polynomial Constitutive Equation

**Authors:**
Tsun-Hui Huang,
Shyue-Cheng Yang,
Chiou-Fen Shieh

**Abstract:**

In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

**Keywords:**
Polynomial constitutive equation,
solitary.

##### 5157 A Novel Deinterlacing Algorithm Based on Adaptive Polynomial Interpolation

**Authors:**
Seung-Won Jung,
Hye-Soo Kim,
Le Thanh Ha,
Seung-Jin Baek,
Sung-Jea Ko

**Abstract:**

**Keywords:**
Deinterlacing,
polynomial interpolation.

##### 5156 Genetic Algorithm and Padé-Moment Matching for Model Order Reduction

**Authors:**
Shilpi Lavania,
Deepak Nagaria

**Abstract:**

A mixed method for model order reduction is presented in this paper. The denominator polynomial is derived by matching both Markov parameters and time moments, whereas numerator polynomial derivation and error minimization is done using Genetic Algorithm. The efficiency of the proposed method can be investigated in terms of closeness of the response of reduced order model with respect to that of higher order original model and a comparison of the integral square error as well.

**Keywords:**
Model Order Reduction (MOR),
control theory,
Markov parameters,
time moments,
genetic algorithm,
Single Input
Single Output (SISO).

##### 5155 Quintic Spline Solution of Fourth-Order Parabolic Equations Arising in Beam Theory

**Authors:**
Reza Mohammadi,
Mahdieh Sahebi

**Abstract:**

**Keywords:**
Fourth-order parabolic equation,
variable coefficient,
polynomial quintic spline,
off-step points,
stability analysis.

##### 5154 Designing FIR Filters with Polynomial Approach

**Authors:**
Sunil Bhooshan,
Vinay Kumar

**Abstract:**

**Keywords:**
FIR filter,
Polynomial.

##### 5153 Blow up in Polynomial Differential Equations

**Authors:**
Rudolf Csikja,
Janos Toth

**Abstract:**

Methods to detect and localize time singularities of polynomial and quasi-polynomial ordinary differential equations are systematically presented and developed. They are applied to examples taken form different fields of applications and they are also compared to better known methods such as those based on the existence of linear first integrals or Lyapunov functions.

**Keywords:**
blow up,
finite escape time,
polynomial ODE,
singularity,
Lotka–Volterra equation,
Painleve analysis,
Ψ-series,
global existence

##### 5152 Design of Digital IIR filters with the Advantages of Model Order Reduction Technique

**Authors:**
K.Ramesh,
A.Nirmalkumar,
G.Gurusamy

**Abstract:**

**Keywords:**
Error index (J),
Factor division method,
IIR filter,
Nyquist plot,
Order reduction.

##### 5151 The BGMRES Method for Generalized Sylvester Matrix Equation AXB − X = C and Preconditioning

**Authors:**
Azita Tajaddini,
Ramleh Shamsi

**Abstract:**

**Keywords:**
Linear matrix equation,
Block GMRES,
matrix Krylov
subspace,
polynomial preconditioner.

##### 5150 On Generalized New Class of Matrix Polynomial Set

**Authors:**
Ghazi S. Kahmmash

**Abstract:**

New generalization of the new class matrix polynomial set have been obtained. An explicit representation and an expansion of the matrix exponential in a series of these matrix are given for these matrix polynomials.

**Keywords:**
Generating functions,
Recurrences relation and Generalization of the new class matrix polynomial set.

##### 5149 A Technique for Improving the Performance of Median Smoothers at the Corners Characterized by Low Order Polynomials

**Authors:**
E. Srinivasan,
D. Ebenezer

**Abstract:**

Median filters with larger windows offer greater smoothing and are more robust than the median filters of smaller windows. However, the larger median smoothers (the median filters with the larger windows) fail to track low order polynomial trends in the signals. Due to this, constant regions are produced at the signal corners, leading to the loss of fine details. In this paper, an algorithm, which combines the ability of the 3-point median smoother in preserving the low order polynomial trends and the superior noise filtering characteristics of the larger median smoother, is introduced. The proposed algorithm (called the combiner algorithm in this paper) is evaluated for its performance on a test image corrupted with different types of noise and the results obtained are included.

**Keywords:**
Image filtering,
detail preservation,
median filters,
nonlinear filters,
order statistics filtering,
Rank order filtering.

##### 5148 Evolutionary Design of Polynomial Controller

**Authors:**
R. Matousek,
S. Lang,
P. Minar,
P. Pivonka

**Abstract:**

**Keywords:**
Evolutionary design,
Genetic algorithms,
PID controller,
Pole placement,
Polynomial controller

##### 5147 Discrete Polynomial Moments and Savitzky-Golay Smoothing

**Authors:**
Paul O'Leary,
Matthew Harker

**Abstract:**

**Keywords:**
Gram polynomials,
Savitzky-Golay Smoothing,
Discrete Polynomial Moments

##### 5146 A Combined Conventional and Differential Evolution Method for Model Order Reduction

**Authors:**
J. S. Yadav,
N. P. Patidar,
J. Singhai,
S. Panda,
C. Ardil

**Abstract:**

In this paper a mixed method by combining an evolutionary and a conventional technique is proposed for reduction of Single Input Single Output (SISO) continuous systems into Reduced Order Model (ROM). In the conventional technique, the mixed advantages of Mihailov stability criterion and continued Fraction Expansions (CFE) technique is employed where the reduced denominator polynomial is derived using Mihailov stability criterion and the numerator is obtained by matching the quotients of the Cauer second form of Continued fraction expansions. Then, retaining the numerator polynomial, the denominator polynomial is recalculated by an evolutionary technique. In the evolutionary method, the recently proposed Differential Evolution (DE) optimization technique is employed. DE 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. The proposed method is illustrated through a numerical example and compared with ROM where both numerator and denominator polynomials are obtained by conventional method to show its superiority.

**Keywords:**
Reduced Order Modeling,
Stability,
Mihailov
Stability Criterion,
Continued Fraction Expansions,
Differential
Evolution,
Integral Squared Error.

##### 5145 Segmentation of Piecewise Polynomial Regression Model by Using Reversible Jump MCMC Algorithm

**Authors:**
Suparman

**Abstract:**

Piecewise polynomial regression model is very flexible model for modeling the data. If the piecewise polynomial regression model is matched against the data, its parameters are not generally known. This paper studies the parameter estimation problem of piecewise polynomial regression model. The method which is used to estimate the parameters of the piecewise polynomial regression model is Bayesian method. Unfortunately, the Bayes estimator cannot be found analytically. Reversible jump MCMC algorithm is proposed to solve this problem. Reversible jump MCMC algorithm generates the Markov chain that converges to the limit distribution of the posterior distribution of piecewise polynomial regression model parameter. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of piecewise polynomial regression model.

**Keywords:**
Piecewise,
Bayesian,
reversible jump MCMC,
segmentation.

##### 5144 Fuzzy Fingerprint Vault using Multiple Polynomials

**Authors:**
Daesung Moon,
Woo-Yong Choi,
Kiyoung Moon

**Abstract:**

Fuzzy fingerprint vault is a recently developed cryptographic construct based on the polynomial reconstruction problem to secure critical data with the fingerprint data. However, the previous researches are not applicable to the fingerprint having a few minutiae since they use a fixed degree of the polynomial without considering the number of fingerprint minutiae. To solve this problem, we use an adaptive degree of the polynomial considering the number of minutiae extracted from each user. Also, we apply multiple polynomials to avoid the possible degradation of the security of a simple solution(i.e., using a low-degree polynomial). Based on the experimental results, our method can make the possible attack difficult 2192 times more than using a low-degree polynomial as well as verify the users having a few minutiae.

**Keywords:**
Fuzzy vault,
fingerprint recognition multiple polynomials.

##### 5143 Computable Function Representations Using Effective Chebyshev Polynomial

**Authors:**
Mohammed A. Abutheraa,
David Lester

**Abstract:**

We show that Chebyshev Polynomials are a practical representation of computable functions on the computable reals. The paper presents error estimates for common operations and demonstrates that Chebyshev Polynomial methods would be more efficient than Taylor Series methods for evaluation of transcendental functions.

**Keywords:**
Approximation Theory,
Chebyshev Polynomial,
Computable Functions,
Computable Real Arithmetic,
Integration,
Numerical Analysis.

##### 5142 Implementation and Analysis of Elliptic Curve Cryptosystems over Polynomial basis and ONB

**Authors:**
Yong-Je Choi,
Moo-Seop Kim,
Hang-Rok Lee,
Ho-Won Kim

**Abstract:**

**Keywords:**
Elliptic Curve Cryptosystem,
Crypto Algorithm,
Polynomial Basis,
Optimal Normal Basis,
Security.

##### 5141 Optimal Image Representation for Linear Canonical Transform Multiplexing

**Authors:**
Navdeep Goel,
Salvador Gabarda

**Abstract:**

**Keywords:**
Chirp signals,
Image multiplexing,
Image
transformation,
Linear canonical transform,
Polynomial
approximation.

##### 5140 Local Error Control in the RK5GL3 Method

**Authors:**
J.S.C. Prentice

**Abstract:**

**Keywords:**
RK5GL3,
RKrGLm,
Runge-Kutta,
Gauss-Legendre,
Hermite interpolating polynomial,
initial value problem,
local error.

##### 5139 A Deterministic Polynomial-time Algorithm for the Clique Problem and the Equality of P and NP Complexity Classes

**Authors:**
Zohreh O. Akbari

**Abstract:**

**Keywords:**
Clique problem,
Deterministic Polynomial-time
Algorithm,
Equality of P and NP Complexity Classes.

##### 5138 Order Reduction using Modified Pole Clustering and Pade Approximations

**Authors:**
C.B. Vishwakarma

**Abstract:**

The authors present a mixed method for reducing the order of the large-scale dynamic systems. In this method, the denominator polynomial of the reduced order model is obtained by using the modified pole clustering technique while the coefficients of the numerator are obtained by Pade approximations. This method is conceptually simple and always generates stable reduced models if the original high-order system is stable. The proposed method is illustrated with the help of the numerical examples taken from the literature.

**Keywords:**
Modified pole clustering,
order reduction,
padeapproximation,
stability,
transfer function.

##### 5137 Lagrange and Multilevel Wavelet-Galerkin with Polynomial Time Basis for Heat Equation

**Authors:**
Watcharakorn Thongchuay,
Puntip Toghaw,
Montri Maleewong

**Abstract:**

**Keywords:**
Galerkin finite element method,
Heat equation ,
Lagrange basis function,
Wavelet basis function.

##### 5136 Numerical Inverse Laplace Transform Using Chebyshev Polynomial

**Authors:**
Vinod Mishra,
Dimple Rani

**Abstract:**

In this paper, numerical approximate Laplace transform inversion algorithm based on Chebyshev polynomial of second kind is developed using odd cosine series. The technique has been tested for three different functions to work efficiently. The illustrations show that the new developed numerical inverse Laplace transform is very much close to the classical analytic inverse Laplace transform.

**Keywords:**
Chebyshev polynomial,
Numerical inverse Laplace transform,
Odd cosine series.

##### 5135 On a New Inverse Polynomial Numerical Scheme for the Solution of Initial Value Problems in Ordinary Differential Equations

**Authors:**
R. B. Ogunrinde

**Abstract:**

**Keywords:**
Differential equations,
Numerical,
Initial value
problem,
Polynomials.

##### 5134 On CR-Structure and F-Structure Satisfying Polynomial Equation

**Authors:**
Manisha Kankarej

**Abstract:**

**Keywords:**
CR-submainfolds,
CR-structure,
Integrability condition & Nijenhuis tensor.

##### 5133 On the Efficiency of Five Step Approximation Method for the Solution of General Third Order Ordinary Differential Equations

**Authors:**
N. M. Kamoh,
M. C. Soomiyol

**Abstract:**

In this work, a five step continuous method for the solution of third order ordinary differential equations was developed in block form using collocation and interpolation techniques of the shifted Legendre polynomial basis function. The method was found to be zero-stable, consistent and convergent. The application of the method in solving third order initial value problem of ordinary differential equations revealed that the method compared favorably with existing methods.

**Keywords:**
Shifted Legendre polynomials,
third order block method,
discrete method,
convergent.