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Sparse Tiling for Stationary Iterative Methods
 INTERNATIONAL JOURNAL OF HIGH PERFORMANCE COMPUTING APPLICATIONS
, 2004
"... In modern computers, a program’s data locality can affect performance significantly. This paper details full sparse tiling, a runtime reordering transformation that improves the data locality for stationary iterative methods such as Gauss–Seidel operating on sparse matrices. In scientific applicati ..."
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Cited by 25 (8 self)
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In modern computers, a program’s data locality can affect performance significantly. This paper details full sparse tiling, a runtime reordering transformation that improves the data locality for stationary iterative methods such as Gauss–Seidel operating on sparse matrices. In scientific
Parallel Linear Stationary Iterative Methods
, 1995
"... . A parallel linear stationary iterative method, defined by domain partitioning and referred to as the JSOR method, is analyzed in this paper. Basic JSOR convergence theorems, including one concerning the optimal relaxation parameter, are presented. JSOR is shown to have a much faster convergence ra ..."
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Cited by 1 (1 self)
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. A parallel linear stationary iterative method, defined by domain partitioning and referred to as the JSOR method, is analyzed in this paper. Basic JSOR convergence theorems, including one concerning the optimal relaxation parameter, are presented. JSOR is shown to have a much faster convergence
Componentwise Error Analysis for Stationary Iterative Methods
, 1993
"... How small can a stationary iterative method for solving a linear system Ax = b make the error and the residual in the presence of rounding errors? We give a componentwise error analysis that provides an answer to this question and we examine the implications for numerical stability. The Jacobi, Gau ..."
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Cited by 11 (6 self)
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How small can a stationary iterative method for solving a linear system Ax = b make the error and the residual in the presence of rounding errors? We give a componentwise error analysis that provides an answer to this question and we examine the implications for numerical stability. The Jacobi
Qualitative Analysis of Some Stationary Iterative Methods
, 1998
"... . Qualitative properties of matrix splitting methods for linear systems with tridiagonal and block tridiagonal StieltjesToeplitz matrices are studied. Two particular splittings, the socalled symmetric tridiagonal splittings and the bidiagonal splittings, are considered, and conditions for qualitat ..."
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. Qualitative properties of matrix splitting methods for linear systems with tridiagonal and block tridiagonal StieltjesToeplitz matrices are studied. Two particular splittings, the socalled symmetric tridiagonal splittings and the bidiagonal splittings, are considered, and conditions
Componentwise Error Estimates for Solutions Obtained by Stationary Iterative Methods∗
"... In stationary iterative methods for solving linear systems Ax = b, the iteration x(k+1) = Hx(k) + c, where H and c are the iteration matrix derived from A and the vector derived from A and b, respectively, is executed for an initial vector x(0). We present a theorem which yields componentwise error ..."
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In stationary iterative methods for solving linear systems Ax = b, the iteration x(k+1) = Hx(k) + c, where H and c are the iteration matrix derived from A and the vector derived from A and b, respectively, is executed for an initial vector x(0). We present a theorem which yields componentwise
Convergence of a Class of Stationary Iterative Methods for Saddle Point Problems
, 2010
"... A unified convergence result is derived for an entire class of stationary iterative methods for solving equality constrained quadratic programs or saddle point problems. This class is constructed from essentially all possible splittings of the n × n submatrix residing in the (1,1)block of the (n+m)× ..."
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A unified convergence result is derived for an entire class of stationary iterative methods for solving equality constrained quadratic programs or saddle point problems. This class is constructed from essentially all possible splittings of the n × n submatrix residing in the (1,1)block of the (n
Existence And Uniqueness Of Splittings For Stationary Iterative Methods With Applications To Alternating Methods
 NUMERISCHE MATHEMATIK
, 1997
"... .iven a nonsingular matrix A, and a matrix T of the same order, under certain very mild conditions, there is a unique splitting A = B \Gamma C, such that T = B \Gamma1 C. Moreover, all properties of the splitting are derived directly from the iteration matrix T . These results do not hold when the ..."
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Cited by 38 (23 self)
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.iven a nonsingular matrix A, and a matrix T of the same order, under certain very mild conditions, there is a unique splitting A = B \Gamma C, such that T = B \Gamma1 C. Moreover, all properties of the splitting are derived directly from the iteration matrix T . These results do not hold when
ON NECESSARY CONDITIONS FOR CONVERGENCE OF STATIONARY ITERATIVE METHODS FOR HERMITIAN SEMIDEFINITE LINEAR SYSTEMS∗
, 2013
"... Abstract. In an earlier paper [SIAM J. Matrix Anal. Appl. vol. 30 (2008), 925–938] we gave sufficient conditions in terms of an energy seminorm for the convergence of stationary iterations for solving linear systems whose coefficient matrix is Hermitian and positive semidefinite. In this paper we sh ..."
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Cited by 1 (1 self)
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Abstract. In an earlier paper [SIAM J. Matrix Anal. Appl. vol. 30 (2008), 925–938] we gave sufficient conditions in terms of an energy seminorm for the convergence of stationary iterations for solving linear systems whose coefficient matrix is Hermitian and positive semidefinite. In this paper we
Comparison of convergence of general stationary iterative methods for singular matrices
 SIAM J. MATRIX ANAL. APPL
, 2002
"... New comparison theorems are presented comparing the asymptotic convergence factor of iterative methods for the solution of consistent (as well as inconsistent) singular systems of linear equations. The asymptotic convergence factor of the iteration matrix T is the quantity γ(T)=max{λ,λ ∈ σ(T),λ � ..."
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Cited by 6 (3 self)
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New comparison theorems are presented comparing the asymptotic convergence factor of iterative methods for the solution of consistent (as well as inconsistent) singular systems of linear equations. The asymptotic convergence factor of the iteration matrix T is the quantity γ(T)=max{λ,λ ∈ σ
Comparison Theorems Of General Stationary Iterative Methods For Singular Matrices
 SIAM J. MATRIX ANAL. APPL
, 2000
"... New comparison theorems are presented comparing the convergence factor of iterative methods for the solution of consistent (as well as inconsistent) singular systems of linear equations. The convergence factor of the iteration matrix T is the quantity (T ) = maxfjj; 2 (T ); 6= 1g, where (T ) is t ..."
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New comparison theorems are presented comparing the convergence factor of iterative methods for the solution of consistent (as well as inconsistent) singular systems of linear equations. The convergence factor of the iteration matrix T is the quantity (T ) = maxfjj; 2 (T ); 6= 1g, where (T
Results 1  10
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675,483