Note on Generating Orthogonal Polynomials and Their Application in Solving Complicated Polynomial Regression Tasks

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11150%2F10%3A10080249" target="_blank" >RIV/00216208:11150/10:10080249 - isvavai.cz</a>

Result on the web

—

DOI - Digital Object Identifier

—

Result language

angličtina

Original language name

Note on Generating Orthogonal Polynomials and Their Application in Solving Complicated Polynomial Regression Tasks

Original language description

The paper deals with efficient numerical solving the proposed statistical model using modern algorithms of numerical linear algebra. In particular, the main ingredients are: Numerically stable generation of vectors of values of orthogonal polynomials (the "design" matrix Psí) based on the MGS Arnoldi algorithm with reorthogonalization, algebraic derivation of the inversion of the matrix Psí'Omega(-1)Psí and, consequently, algebraic derivation of the solution of the system of normal equations, and, finally, efficient computation of testing quantities based on the Cholesky decomposition of relatively small matrices. The techniques presented in this paper represent economized way of solving the problem. From the point of view of practical computing, we save the computer memory as well as the time requirements. We manipulate only with small matrices, we do not compute inversions of large matrices and we do not even need to solve linear algebraic systems with large matrices.

Czech name

—

Czech description

—

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BB - Applied statistics, operational research

OECD FORD branch

—

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2010

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

International Journal of Mathematics and Computation

ISSN

0974-570X

e-ISSN

—

Volume of the periodical

7

Issue of the periodical within the volume

J10

Country of publishing house

IN - INDIA

Number of pages

23

Pages from-to

—

UT code for WoS article

—

EID of the result in the Scopus database

—