nearness problem;
iterative methods;
short term recurrence;
D O I:
10.1137/S0036142999363620
中图分类号:
O29 [应用数学];
学科分类号:
070104 ;
摘要:
We consider a matrix nearness problem arising from an analysis of the speed of convergence of GMREs for solving a linear system Ax = b with A is an element of C-nxn and b is an element of C-n. More precisely, denoting by F-k the set of matrices of rank k at most, we solve [GRAPHICS] where S subset of C-nxn denotes the set of matrices of the form e(i theta) H - lambdaI with theta is an element of [0, 2 pi), lambda is an element of C, and H belonging to the set of Hermitian matrices. As to iterative methods, the set S is of interest in a larger context. To give an example, having a regular splitting A = S + F-k of A, the system Ax = b can be solved using a (k+3)-term recurrence with inner-outer iterations.
机构:
PDPM Indian Inst Informat Technol Design & Mfg, Math Discipline, Dumna Rd, Jabalpur 482005, MP, IndiaPDPM Indian Inst Informat Technol Design & Mfg, Math Discipline, Dumna Rd, Jabalpur 482005, MP, India
Kumar, Bharat
Deepmala
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机构:
PDPM Indian Inst Informat Technol Design & Mfg, Math Discipline, Dumna Rd, Jabalpur 482005, MP, IndiaPDPM Indian Inst Informat Technol Design & Mfg, Math Discipline, Dumna Rd, Jabalpur 482005, MP, India
Deepmala
Dutta, A.
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机构:
Jadavpur Univ, Dept Math, 188 Raja SC Mallick Rd, Jadavpur 700032, West Bengal, IndiaPDPM Indian Inst Informat Technol Design & Mfg, Math Discipline, Dumna Rd, Jabalpur 482005, MP, India
Dutta, A.
Das, A. K.
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机构:
Indian Stat Inst, SQC & Unit, 203 BT Rd, Kolkata 700108, West Bengal, IndiaPDPM Indian Inst Informat Technol Design & Mfg, Math Discipline, Dumna Rd, Jabalpur 482005, MP, India
机构:
Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Paseo Alfonso XIII, 52, CartagenaDepartamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Paseo Alfonso XIII, 52, Cartagena
Amat S.
Ezquerro J.A.
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Department of Mathematics and Computation, University of La Rioja, C/Luis de Ulloa s/n, LogroñoDepartamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Paseo Alfonso XIII, 52, Cartagena
Ezquerro J.A.
Hernández-Verón M.A.
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机构:
Department of Mathematics and Computation, University of La Rioja, C/Luis de Ulloa s/n, LogroñoDepartamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Paseo Alfonso XIII, 52, Cartagena