A reduction of a quaternion-valued matrix

Result code in 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>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

A reduction of a quaternion-valued matrix

Original language description

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

Czech name

A continuation of singular values of a parameter-dependent matrix

Czech description

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

Type

O - Miscellaneous

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2005

Confidentiality

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