A NEW BCR METHOD FOR COUPLED OPERATOR EQUATIONS WITH SUBMATRIX CONSTRAINT

Wenling Wang; Caiqin Song; Wenli Wang

doi:10.11948/20230106

2024 Volume 14 Issue 4

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Wenling Wang, Caiqin Song, Wenli Wang. A NEW BCR METHOD FOR COUPLED OPERATOR EQUATIONS WITH SUBMATRIX CONSTRAINT[J]. Journal of Applied Analysis & Computation, 2024, 14(4): 2002-2036. doi: 10.11948/20230106

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Wenling Wang, Caiqin Song, Wenli Wang. A NEW BCR METHOD FOR COUPLED OPERATOR EQUATIONS WITH SUBMATRIX CONSTRAINT[J]. Journal of Applied Analysis & Computation, 2024, 14(4): 2002-2036. doi: 10.11948/20230106

A NEW BCR METHOD FOR COUPLED OPERATOR EQUATIONS WITH SUBMATRIX CONSTRAINT

1.
School of Mathematical Sciences, University of Jinan, Jinan 250022, China
2.
School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China

Author Bio: Email: wangwenling_dp@163.com(W. Wang); Email: wenliwang_cba@163.com(W. Wang)
Corresponding author: Email: songcaiqin1983@163.com(C. Song)

Abstract

Abstract

In the present work, a new biconjugate residual (BCR) algorithm is proposed in order to compute the constraint solution of the coupled operator equations, in which the constraint solution include symmetric solution, reflective solution, centrosymmetric solution and anti-centrosymmetric solution as special cases. When the studied coupled operator equations are consistent, it is proved that constraint solutions can be convergent to the exact solutions if giving any initial complex matrices or real matrices. In addition, when the studied coupled operator equations are not consistent, the least norm constraint solutions above can also be computed by selecting any initial matrices. Finally, some numerical examples are provided for illustrating the effectiveness and superiority of new proposed method.
- Operator matrix equations /
- BCR algorithm /
- least-norm constraint solutions /
- submatrix constraint
MSC: 13F35, 15A06, 41A29, 47A05, 65F30

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References

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