About: Note on generating orthogonal polynomials and their application in solving complicated polynomial regression tasks

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	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 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 on 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 the practice are discussed. 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 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 on 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 the practice are discussed. (en)
Title	Note on generating orthogonal polynomials and their application in solving complicated polynomial regression tasks Note on generating orthogonal polynomials and their application in solving complicated polynomial regression tasks (en)
skos:prefLabel	Note on generating orthogonal polynomials and their application in solving complicated polynomial regression tasks Note on generating orthogonal polynomials and their application in solving complicated polynomial regression tasks (en)
skos:notation	RIV/00209805:_____/10:#0000123!RIV11-GA0-00209805
http://linked.open...avai/riv/aktivita	I P V Z
http://linked.open...avai/riv/aktivity	I, P(GAP304/10/0868), P(NS9812), V, Z(AV0Z10300504), Z(AV0Z10750506)
http://linked.open...iv/cisloPeriodika	J10
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Vojtěšek, Bořivoj Bouchal, Pavel Nenutil, Rudolf
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Masarykův onkologický ústav
http://linked.open...dnocenehoVysledku	275158
http://linked.open...ai/riv/idVysledku	RIV/00209805:_____/10:#0000123
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	polynomial regression, orthogonalization, numerical mathods, markers, biomarkers (en)
http://linked.open.../riv/klicoveSlovo	orthogonalization biomarkers markers polynomial regression numerical mathods
http://linked.open...odStatuVydavatele	IN - Indická republika
http://linked.open...ontrolniKodProRIV	[6774226D0643]
http://linked.open...i/riv/nazevZdroje	International journal of mathematics and computation
http://linked.open...in/vavai/riv/obor	FD
http://linked.open...ichTvurcuVysledku	3 (xsd:int)
http://linked.open...cetTvurcuVysledku	8 (xsd:int)
http://linked.open...vavai/riv/projekt	The proteomics-based study on molecular mechanisms of early lymph node metastases formation in low-grade breast cancer Elucidating the role of ubiquitin-chaperone degradation machinery in cancer and modulating its biochemical functions using targeted chaperone inhibitors
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	7
http://linked.open...iv/tvurceVysledku	Vojtěšek, Bořivoj Bouchal, Pavel Knížek, J. Nenutil, Rudolf
http://linked.open...n/vavai/riv/zamer	Informatika pro informační společnost: modely, algoritmy, aplikace Pokročilé matematické metody získávání, zpracování a využití informací a znalostí ve složitých a nedeterministických systémech
issn	0974-5718
number of pages	13 (xsd:int)

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