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This paper concerns with exploiting an oblique projection technique to solve a general class of large and sparse least squares problem over symmetric arrowhead matrices. As a matter of fact, we develop the conjugate gradient least squares (CGLS) algorithm to obtain the minimum norm symmetric arrowhead least squares solution of the general coupled matrix equations. Furthermore, an approach is offered for computing the optimal approximate symmetric arrowhead solution of the mentioned least squares problem corresponding to a given arbitrary matrix group. In addition, the minimization property of the proposed algorithm is established by utilizing the feature of approximate solutions derived by the projection method. Finally, some numerical experiments are examined which reveal the applicability and feasibility of the handled algorithm.
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참고문헌 (26)
참고문헌 신청
[학술
A. Bj¨orck / 1996 / Numerical Methods for Least Squares Problems / SIAM
A. Bouhamidi / 2008 / A note on the numerical approximate solutions for gener-alized Sylvester matrix equations with applications / Appl. Math. Comput 206 (2) : 687 ~ 694
A. El Guennouni / 2002 / Block Krylov subspace methods for solving large Sylvester equations / Numer. Algorithms 29 (1-3) : 75 ~ 96
B. Parlett / 1980 / The Symmetric Eigenvalue Problem / Prentice-Hall
A. Bj¨orck / 1996 / Numerical Methods for Least Squares Problems / SIAM
A. Bouhamidi / 2008 / A note on the numerical approximate solutions for gener-alized Sylvester matrix equations with applications / Appl. Math. Comput 206 (2) : 687 ~ 694
A. El Guennouni / 2002 / Block Krylov subspace methods for solving large Sylvester equations / Numer. Algorithms 29 (1-3) : 75 ~ 96
B. Parlett / 1980 / The Symmetric Eigenvalue Problem / Prentice-Hall
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