Accurate solutions of structured generalized Kronecker product linear systems

被引:11
作者
Yang, Zhao [1 ]
Huang, Rong [2 ]
Zhu, Wei [1 ]
Liu, Jianzhou [3 ]
机构
[1] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China
[2] Hunan Univ Sci & Technol, Sch Math & Computat Sci, Xiangtan 411201, Hunan, Peoples R China
[3] Xiangtan Univ, Hunan Key Lab Computat & Simulat Sci & Engn, Xiangtan 411105, Hunan, Peoples R China
关键词
Componentwise forward errors; Generalized Kronecker product linear systems; Bivariate interpolation problems; Generalized Vandermonde matrices; BIVARIATE POLYNOMIAL INTERPOLATION; COLLOCATION MATRICES; TOTAL POSITIVITY; COMPUTATIONS; DECOMPOSITION; EIGENVALUES; SOLVABILITY; ALGORITHM;
D O I
10.1007/s11075-020-00988-5
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we consider the generalized Kronecker product (GKP) linear system associated with a class of consecutive-rank-descending (CRD) matrices arising from bivariate interpolation problems. Relying on the sign sequences of CRD matrices, we show that the associated GKP linear system is accurately solved with an "ideal" componentwise forward error. In particular, a pleasantly small componentwise relative forward error is provided to illustrate that each component of the solution is computed to high relative accuracy. We then present the sign sequences of generalized Vandermonde matrices to show that the associated GKP linear system is accurately solved with the desired componentwise forward errors. Numerical experiments are performed to confirm the high relative accuracy.
引用
收藏
页码:797 / 818
页数:22
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