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of Complex Symmetric Linear Systems ∗
, 2009
"... In this paper, we introduce and analyze a modification of the Hermitian and skewHermitian splitting iteration method for solving a broad class of complex symmetric linear systems. We show that the modified Hermitian and skewHermitian splitting (MHSS) iteration method is unconditionally convergent. ..."
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In this paper, we introduce and analyze a modification of the Hermitian and skewHermitian splitting iteration method for solving a broad class of complex symmetric linear systems. We show that the modified Hermitian and skewHermitian splitting (MHSS) iteration method is unconditionally convergent
Preconditioning complex symmetric linear systems
"... A new polynomial preconditioner for symmetric complex linear systems based on Hermitian and skewHermitian splitting (HSS) for complex symmetric linear systems is herein presented. It applies to Conjugate Orthogonal Conjugate Gradient (COCG) or Conjugate Orthogonal Conjugate Residual (COCR) iterativ ..."
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A new polynomial preconditioner for symmetric complex linear systems based on Hermitian and skewHermitian splitting (HSS) for complex symmetric linear systems is herein presented. It applies to Conjugate Orthogonal Conjugate Gradient (COCG) or Conjugate Orthogonal Conjugate Residual (COCR
Iterative Solution of Symmetric Linear Systems∗
, 2008
"... those of the authors and not those of the Department. The Working Paper series is designed to divulge preliminary or incomplete work, circulated to favour discussion and comments. Citation of this paper should consider its provisional nature. Notes on a 3term Conjugacy Recurrence for the ..."
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those of the authors and not those of the Department. The Working Paper series is designed to divulge preliminary or incomplete work, circulated to favour discussion and comments. Citation of this paper should consider its provisional nature. Notes on a 3term Conjugacy Recurrence for the
Simultaneous preconditioning and symmetrization of nonsymmetric linear systems
, 2008
"... Motivated by the theory of selfduality which provides a variational formulation and resolution for non selfadjoint partial differential equations [6, 7], we propose new templates for solving large nonsymmetric linear systems. The method consists of combining a new scheme that simultaneously preco ..."
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Motivated by the theory of selfduality which provides a variational formulation and resolution for non selfadjoint partial differential equations [6, 7], we propose new templates for solving large nonsymmetric linear systems. The method consists of combining a new scheme that simultaneously
Symmetric Linear Systems with Perturbed Input Data
 NUMERICAL METHODS AND ERROR BOUNDS. PROCEEDINGS OF THE IMACSGAMM INTERNATIONAL SYMPOSIUM ON NUMERICAL METHODS AND ERROR BOUNDS
, 1996
"... We present a method for constructing a set of inequalities which describe completely the so–called symmetric solution set Ssym:= {x ∈ R n  Ax = b, A = A T ∈ [A], b ∈ [b]}. Here, [A] is an n × n interval matrix satisfying [A] = [A] T and [b] is an interval vector with n components. ..."
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Cited by 5 (5 self)
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We present a method for constructing a set of inequalities which describe completely the so–called symmetric solution set Ssym:= {x ∈ R n  Ax = b, A = A T ∈ [A], b ∈ [b]}. Here, [A] is an n × n interval matrix satisfying [A] = [A] T and [b] is an interval vector with n components.
Two Algorithms For Symmetric Linear Systems With Multiple RightHand Sides
, 1998
"... In this paper, we investigate the block Lanczos algorithm for solving large sparse symmetric linear systems with multiple righthand sides, and show how to incorporate deflation to drop converged linear systems using a natural convergence criterion, and present an adaptive block Lanczos algorithm. W ..."
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Cited by 2 (1 self)
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In this paper, we investigate the block Lanczos algorithm for solving large sparse symmetric linear systems with multiple righthand sides, and show how to incorporate deflation to drop converged linear systems using a natural convergence criterion, and present an adaptive block Lanczos algorithm
Exploiting Zeros on the Diagonal in the Direct Solution of Indefinite Sparse Symmetric Linear Systems
, 1995
"... We describe the design of a new code for the solution of sparse indefinite symmetric linear systems of equations. The principal difference between this new code and earlier work lies in the exploitation of the additional sparsity available when the matrix has a significant number of zero diagona ..."
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Cited by 29 (10 self)
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We describe the design of a new code for the solution of sparse indefinite symmetric linear systems of equations. The principal difference between this new code and earlier work lies in the exploitation of the additional sparsity available when the matrix has a significant number of zero
Efficient preconditioning for sequences of parametric complex symmetric linear systems
 Electronic Transactions on Numerical Mathematics
"... Abstract. Solution of sequences of complex symmetric linear systems of the form Ajxj = bj, j = 0,..., s, Aj = A + αjEj, A Hermitian, E0,..., Es complex diagonal matrices and α0,..., αs scalar complex parameters arise in a variety of challenging problems. This is the case of time dependent PDEs; latt ..."
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Cited by 12 (2 self)
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Abstract. Solution of sequences of complex symmetric linear systems of the form Ajxj = bj, j = 0,..., s, Aj = A + αjEj, A Hermitian, E0,..., Es complex diagonal matrices and α0,..., αs scalar complex parameters arise in a variety of challenging problems. This is the case of time dependent PDEs
A Generalized Preconditioned MPHSS Method for a Class of Complex Symmetric Linear System
"... Abstract—In this paper, with the MHSS and preconditioned MHSS methods, we get a generalized preconditioned MHSS method with a kind of complex symmetric linear systems. This method is a twoparameter iteration process, which can optimize the iterative process. The sequence of iterative produced by th ..."
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Abstract—In this paper, with the MHSS and preconditioned MHSS methods, we get a generalized preconditioned MHSS method with a kind of complex symmetric linear systems. This method is a twoparameter iteration process, which can optimize the iterative process. The sequence of iterative produced
Results 1  10
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2,758,925