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%2F60076658%3A12510%2F10%3A00012341" target="_blank" >RIV/60076658:12510/10:00012341 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/67985807:_____/10:00351359 RIV/67985556:_____/10:00351359 RIV/00209805:_____/10:#0000123

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 ) based on the MGS Arnoldi algorithm with reorthogonalization, - algebraic derivation of the inversion of the matrix and, consequently, algebraic derivation of the solution of the system of normal equations, - and, finally, efficientcomputation 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 ) based on the MGS Arnoldi algorithm with reorthogonalization, - algebraic derivation of the inversion of the matrix and, consequently, algebraic derivation of the solution of the system of normal equations, - and, finally, efficientcomputation 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

IN - Informatika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

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

0974-5718

e-ISSN

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Svazek periodika

7

Číslo periodika v rámci svazku

J10

Stát vydavatele periodika

IN - Indická republika

Počet stran výsledku

13

Strana od-do

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Kód UT WoS článku

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EID výsledku v databázi Scopus

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