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Hermitian tridiagonal solution with the least norm to quaternionic least squares problem. (English) Zbl 1205.81086
Summary: Quaternionic least squares (QLS) is an efficient method for solving approximate problems in quaternionic quantum theory. In view of the extensive applications of Hermitian tridiagonal matrices in physics, in this paper we list some properties of basis matrices and subvectors related to tridiagonal matrices, and give an iterative algorithm for finding Hermitian tridiagonal solution with the least norm to the quaternionic least squares problem by making the best use of structure of real representation matrices, we also propose a preconditioning strategy for the Algorithm LSQR-Q in {\it M. Wang, M. Wei} and {\it Y. Feng} [ibid. 179, No. 4, 203--207 (2008; Zbl 1197.81138)] and our algorithm. Numerical experiments are provided to verify the effectiveness of our method.

81Q10Selfadjoint operator theory in quantum theory, including spectral analysis
15B33Matrices over special rings (quaternions, finite fields, etc.)
81-08Computational methods (quantum theory)
65D99Numerical approximation
93E24Least squares and related methods in stochastic control
Full Text: DOI
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