**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**8657

# Search results for: linear and polynomial model.

##### 8657 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

##### 8656 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.

##### 8655 Empirical Statistical Modeling of Rainfall Prediction over Myanmar

**Authors:**
Wint Thida Zaw,
Thinn Thu Naing

**Abstract:**

**Keywords:**
Polynomial Regression,
Rainfall Forecasting,
Statistical forecasting.

##### 8654 Discrete Polynomial Moments and Savitzky-Golay Smoothing

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

**Abstract:**

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

##### 8653 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.

##### 8652 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.

##### 8651 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.

##### 8650 Factoring a Polynomial with Multiple-Roots

**Authors:**
Feng Cheng Chang

**Abstract:**

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

##### 8649 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.

##### 8648 Designing FIR Filters with Polynomial Approach

**Authors:**
Sunil Bhooshan,
Vinay Kumar

**Abstract:**

**Keywords:**
FIR filter,
Polynomial.

##### 8647 A Comparison of the Sum of Squares in Linear and Partial Linear Regression Models

**Authors:**
Dursun Aydın

**Abstract:**

**Keywords:**
Partial Linear Regression Model,
Linear RegressionModel,
Residuals,
Deviance,
Smoothing Spline.

##### 8646 Computational Aspects of Regression Analysis of Interval Data

**Authors:**
Michal Cerny

**Abstract:**

We consider linear regression models where both input data (the values of independent variables) and output data (the observations of the dependent variable) are interval-censored. We introduce a possibilistic generalization of the least squares estimator, so called OLS-set for the interval model. This set captures the impact of the loss of information on the OLS estimator caused by interval censoring and provides a tool for quantification of this effect. We study complexity-theoretic properties of the OLS-set. We also deal with restricted versions of the general interval linear regression model, in particular the crisp input – interval output model. We give an argument that natural descriptions of the OLS-set in the crisp input – interval output cannot be computed in polynomial time. Then we derive easily computable approximations for the OLS-set which can be used instead of the exact description. We illustrate the approach by an example.

**Keywords:**
Linear regression,
interval-censored data,
computational complexity.

##### 8645 A Mathematical Model Approach Regarding the Children’s Height Development with Fractional Calculus

**Authors:**
Nisa Özge Önal,
Kamil Karaçuha,
Göksu Hazar Erdinç,
Banu Bahar Karaçuha,
Ertuğrul Karaçuha

**Abstract:**

The study aims to use a mathematical approach with the fractional calculus which is developed to have the ability to continuously analyze the factors related to the children’s height development. Until now, tracking the development of the child is getting more important and meaningful. Knowing and determining the factors related to the physical development of the child any desired time would provide better, reliable and accurate results for childcare. In this frame, 7 groups for height percentile curve (3th, 10th, 25th, 50th, 75th, 90th, and 97th) of Turkey are used. By using discrete height data of 0-18 years old children and the least squares method, a continuous curve is developed valid for any time interval. By doing so, in any desired instant, it is possible to find the percentage and location of the child in Percentage Chart. Here, with the help of the fractional calculus theory, a mathematical model is developed. The outcomes of the proposed approach are quite promising compared to the linear and the polynomial method. The approach also yields to predict the expected values of children in the sense of height.

**Keywords:**
Children growth percentile,
children physical development,
fractional calculus,
linear and polynomial model.

##### 8644 Development of Admire Longitudinal Quasi-Linear Model by using State Transformation Approach

**Authors:**
Jianqiao. Yu,
Jianbo. Wang,
Xinzhen. He

**Abstract:**

This paper presents a longitudinal quasi-linear model for the ADMIRE model. The ADMIRE model is a nonlinear model of aircraft flying in the condition of high angle of attack. So it can-t be considered to be a linear system approximately. In this paper, for getting the longitudinal quasi-linear model of the ADMIRE, a state transformation based on differentiable functions of the nonscheduling states and control inputs is performed, with the goal of removing any nonlinear terms not dependent on the scheduling parameter. Since it needn-t linear approximation and can obtain the exact transformations of the nonlinear states, the above-mentioned approach is thought to be appropriate to establish the mathematical model of ADMIRE. To verify this conclusion, simulation experiments are done. And the result shows that this quasi-linear model is accurate enough.

**Keywords:**
quasi-linear model,
simulation,
state transformation approach,
the ADMIRE model.

##### 8643 Orthogonal Polynomial Density Estimates: Alternative Representation and Degree Selection

**Authors:**
Serge B. Provost,
Min Jiang

**Abstract:**

**Keywords:**
kernel density estimation,
orthogonal polynomials,
moment-based methodologies,
density approximation.

##### 8642 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.

##### 8641 Behavioral Modeling Accuracy for RF Power Amplifier with Memory Effects

**Authors:**
Chokri Jebali,
Noureddine Boulejfen,
Ali Gharsallah,
Fadhel M. Ghannouchi

**Abstract:**

**Keywords:**
power amplifier,
orthogonal model,
polynomialmodel ,
memory effects.

##### 8640 A Hybrid Model of ARIMA and Multiple Polynomial Regression for Uncertainties Modeling of a Serial Production Line

**Authors:**
Amir Azizi,
Amir Yazid b. Ali,
Loh Wei Ping,
Mohsen Mohammadzadeh

**Abstract:**

**Keywords:**
ARIMA,
multiple polynomial regression,
production
throughput,
uncertainties

##### 8639 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

##### 8638 GMDH Modeling Based on Polynomial Spline Estimation and Its Applications

**Authors:**
LI qiu-min,
TIAN yi-xiang,
ZHANG gao-xun

**Abstract:**

GMDH algorithm can well describe the internal structure of objects. In the process of modeling, automatic screening of model structure and variables ensure the convergence rate.This paper studied a new GMDH model based on polynomial spline stimation. The polynomial spline function was used to instead of the transfer function of GMDH to characterize the relationship between the input variables and output variables. It has proved that the algorithm has the optimal convergence rate under some conditions. The empirical results show that the algorithm can well forecast Consumer Price Index (CPI).

**Keywords:**
spline,
GMDH,
nonparametric,
bias,
forecast.

##### 8637 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.

##### 8636 Comparison of Polynomial and Radial Basis Kernel Functions based SVR and MLR in Modeling Mass Transfer by Vertical and Inclined Multiple Plunging Jets

**Abstract:**

**Keywords:**
Mass transfer,
multiple plunging jets,
polynomial
and radial basis kernel functions,
Support Vector Regression.

##### 8635 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.

##### 8634 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).

##### 8633 Some Preconditioners for Block Pentadiagonal Linear Systems Based on New Approximate Factorization Methods

**Authors:**
Xian Ming Gu,
Ting Zhu Huang,
Hou Biao Li

**Abstract:**

In this paper, getting an high-efficiency parallel algorithm to solve sparse block pentadiagonal linear systems suitable for vectors and parallel processors, stair matrices are used to construct some parallel polynomial approximate inverse preconditioners. These preconditioners are appropriate when the desired target is to maximize parallelism. Moreover, some theoretical results about these preconditioners are presented and how to construct preconditioners effectively for any nonsingular block pentadiagonal H-matrices is also described. In addition, the availability of these preconditioners is illustrated with some numerical experiments arising from two dimensional biharmonic equation.

**Keywords:**
Parallel algorithm,
Pentadiagonal matrix,
Polynomial
approximate inverse,
Preconditioners,
Stair matrix.

##### 8632 Nonlinear Model Predictive Control for Solid Oxide Fuel Cell System Based On Wiener Model

**Authors:**
T. H. Lee,
J. H. Park,
S. M. Lee,
S. C. Lee

**Abstract:**

In this paper, we consider Wiener nonlinear model for solid oxide fuel cell (SOFC). The Wiener model of the SOFC consists of a linear dynamic block and a static output non-linearity followed by the block, in which linear part is approximated by state-space model and the nonlinear part is identified by a polynomial form. To control the SOFC system, we have to consider various view points such as operating conditions, another constraint conditions, change of load current and so on. A change of load current is the significant one of these for good performance of the SOFC system. In order to keep the constant stack terminal voltage by changing load current, the nonlinear model predictive control (MPC) is proposed in this paper. After primary control method is designed to guarantee the fuel utilization as a proper constant, a nonlinear model predictive control based on the Wiener model is developed to control the stack terminal voltage of the SOFC system. Simulation results verify the possibility of the proposed Wiener model and MPC method to control of SOFC system.

**Keywords:**
SOFC,
model predictive control,
Wiener model.

##### 8631 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.

##### 8630 Identification of Nonlinear Systems Structured by Hammerstein-Wiener Model

**Authors:**
A. Brouri,
F. Giri,
A. Mkhida,
F. Z. Chaoui,
A. Elkarkri,
M. L. Chhibat

**Abstract:**

Standard Hammerstein-Wiener models consist of a linear subsystem sandwiched by two memoryless nonlinearities. The problem of identifying Hammerstein-Wiener systems is addressed in the presence of linear subsystem of structure totally unknown and polynomial input and output nonlinearities. Presently, the system nonlinearities are allowed to be noninvertible. The system identification problem is dealt by developing a two-stage frequency identification method. First, the parameters of system nonlinearities are identified. In the second stage, a frequency approach is designed to estimate the linear subsystem frequency gain. All involved estimators are proved to be consistent.

**Keywords:**
Nonlinear system identification,
Hammerstein systems,
Wiener systems,
frequency identification.

##### 8629 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.

##### 8628 Ensembling Adaptively Constructed Polynomial Regression Models

**Authors:**
Gints Jekabsons

**Abstract:**

**Keywords:**
Basis function construction,
heuristic search,
modelensembles,
polynomial regression.