Algebraic algorithms for least squares problem in quaternionic quantum theory

Quaternionic least squares (QLS) problem is one method of solving overdetermined sets of quaternion linear equations A X ≈ B that is appropriate when there is error in the matrix B. In this paper, by means of complex representation of a quaternion matrix, we introduce a concept of norm of quaternion...

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Vydané v:	Computer physics communications Ročník 176; číslo 7; s. 481 - 485
Hlavní autori:	Jiang, Tongsong, Chen, Li
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier B.V 01.04.2007
Predmet:	Algorithm Least squares Quaternion matrix Quaternionic quantum theory Quaternionic quantum theory Quaternion matrix 03.65.Fd Least squares Algorithm 02.10.Yn 04.25.Nx
ISSN:	0010-4655, 1879-2944
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Popis
Shrnutí:	Quaternionic least squares (QLS) problem is one method of solving overdetermined sets of quaternion linear equations A X ≈ B that is appropriate when there is error in the matrix B. In this paper, by means of complex representation of a quaternion matrix, we introduce a concept of norm of quaternion matrices, discuss singular values and generalized inverses of a quaternion matrix, study the QLS problem and derive two algebraic methods for finding solutions of the QLS problem in quaternionic quantum theory.
ISSN:	0010-4655 1879-2944
DOI:	10.1016/j.cpc.2006.12.005