Počet záznamů: 1
Note on Generating Orthogonal Polynomials and Their Application in Solving Complicated Polynomial Regression Tasks
- 1.
SYSNO ASEP 0351359 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Ostatní články Název Note on Generating Orthogonal Polynomials and Their Application in Solving Complicated Polynomial Regression Tasks Tvůrce(i) Knížek, J. (CZ)
Tichý, Petr (UIVT-O) SAI, RID, ORCID
Beránek, L. (CZ)
Šindelář, Jan (UTIA-B)
Vojtěšek, B. (CZ)
Bouchal, P. (CZ)
Nenutil, R. (CZ)
Dedík, O. (CZ)Zdroj.dok. International Journal of Mathematics and Computation - ISSN 0974-5718
Roč. 7, č. 10 (2010), s. 48-60Poč.str. 13 s. Jazyk dok. eng - angličtina Země vyd. IN - Indie Klíč. slova polynomial regression ; orthogonalization ; numerical methods ; markers ; biomarkers Vědní obor RIV BA - Obecná matematika CEZ AV0Z10300504 - UIVT-O (2005-2011) AV0Z10750506 - UTIA-B (2005-2011) Anotace In this paper, we describe efficient algorithms for computing solutions of numerically exacting parts of used complicated polynomial regression tasks. In particular, we use a numerically stable way of generating the values of normalized orthogonal polynomials on a discrete set of points; we use “the Arnoldi algorithm with reorthogonalization”, which is the key ingredient of our approach. The generated vectors can then be considered orthogonal also in finite precision arithmetic (up to a small inaccuracy proportional to machine precision). We then use the special algebraic structure of the covariance matrix to find algebraically the inversion of the matrix of the system of normal equations. Therefore, we do not need to compute numerically the inversion of the covariance matrix and we do not even need to solve the system of normal equations numerically. Some consequences of putting the algorithms mentioned into practice are discussed. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2011
Počet záznamů: 1