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

Kód výsledku v 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>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BB - Aplikovaná statistika, operační výzkum

OECD FORD obor

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Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2010

Kód důvěrnosti údajů

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

Název periodika

International Journal of Mathematics and Computation

ISSN

0974-570X

e-ISSN

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Svazek periodika

7

Číslo periodika v rámci svazku

J10

Stát vydavatele periodika

IN - Indická republika

Počet stran výsledku

23

Strana od-do

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Kód UT WoS článku

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EID výsledku v databázi Scopus

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