A continuation of singular values of a parameter-dependent matrix

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60461373%3A22340%2F05%3A00014847" target="_blank" >RIV/60461373:22340/05:00014847 - 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

A reduction of a quaternion-valued matrix

Popis výsledku v původním jazyce

Since arithmetic operations with quaternions are very costly it is desirable to reduce the number of arithmetic operations with quaternions. The Fast Givens' transformation, known for the real case, can also be defined for quaternion valued matrices, inparticular, a reduction to upper Hessenberg form of general quaternion valued matrices will be presented, including a numerical example. We also show that the application of the Fast Givens' transformation in the complex case and in the quaternion case is not as favorable as in the real case with respect to (relative) savings in arithmetic operations. We always consider two alternative forms of Fast Givens' transformations in order to control stability and we also present a formula where the essential information is stored in only one variable. This is apparently even new for the real case. We begin with some introduction into the field of quaternions. In the end we will present some results concerning the computation of square roots of

Název v anglickém jazyce

A reduction of a quaternion-valued matrix

Popis výsledku anglicky

Since arithmetic operations with quaternions are very costly it is desirable to reduce the number of arithmetic operations with quaternions. The Fast Givens' transformation, known for the real case, can also be defined for quaternion valued matrices, inparticular, a reduction to upper Hessenberg form of general quaternion valued matrices will be presented, including a numerical example. We also show that the application of the Fast Givens' transformation in the complex case and in the quaternion case is not as favorable as in the real case with respect to (relative) savings in arithmetic operations. We always consider two alternative forms of Fast Givens' transformations in order to control stability and we also present a formula where the essential information is stored in only one variable. This is apparently even new for the real case. We begin with some introduction into the field of quaternions. In the end we will present some results concerning the computation of square roots of

Druh

O - Ostatní výsledky

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2005

Kód důvěrnosti údajů

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