A real structure-preserving algorithm based on the quaternion QR decomposition for the quaternion equality constrained least squares problem

In this paper, we consider the computational problem of the quaternion equality constrained least squares problem. First, applying the quaternion QR decomposition and an equivalence problem of the quaternion equality constrained least squares problem, we obtain the expressions of the general solutio...

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Vydáno v:Numerical algorithms Ročník 91; číslo 4; s. 1815 - 1827
Hlavní autoři: Zhang, Fengxia, Zhao, Jianli
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.12.2022
Springer Nature B.V
Témata:
Algebra
Algorithms
Computer Science
Decomposition
Floating point arithmetic
Least squares method
Numeric Computing
Numerical Analysis
Original Paper
Quaternions
Representations
Theory of Computation
Real representation matrix
Quaternion equality constrained least squares problem
Quaternion QR decomposition
Real structure-preserving algorithm
ISSN:1017-1398, 1572-9265
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Shrnutí:In this paper, we consider the computational problem of the quaternion equality constrained least squares problem. First, applying the quaternion QR decomposition and an equivalence problem of the quaternion equality constrained least squares problem, we obtain the expressions of the general solution and the minimal norm solution of the quaternion equality constrained least squares problem. And then by using the real representation matrices of quaternion matrices, the special structure of the real representation matrices and the real structure-preserving algorithm of the quaternion QR decomposition, we purpose a real structure-preserving algorithm for the minimal norm solution of the quaternion equality constrained least squares problem. The purposed algorithm only involves real algebraic operations, and the number of real floating-point operations and assignments has been minimized. Finally, we give two examples, which show that our purposed algorithm is more efficient and time-saving than direct computation in the quaternion Toolbox for Matlab.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-022-01323-w