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Equality constrained least squares problem over quaternion field

✍ Scribed by Tongsong Jiang; Musheng Wei

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
381 KB
Volume
16
Category
Article
ISSN
0893-9659

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✦ Synopsis

By

using complex representation and GSVD of quaternion matrices, we define the norm of quatemion matrices, study the equality constrained least squares problem of quatemion matrices, give the necessary and sufficient conditions for the quatemion equality constrained least squarea problem to have solutions, and finally derive a practical algorithm.

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## Abstract In this paper, two new matrix‐form iterative methods are presented to solve the least‐squares problem: and matrix nearness problem: where matrices $A\in R^{p\times n\_1},B\in R^{n\_2\times q},C\in R^{p\times m\_1},D\in R^{m\_2\times q},E\in R^{p\times q},\widetilde{X}\in R^{n\_1\time