Add to ORKGThis paper is concerned with the problem of verifying the accuracy of an approximate solution of a sparse linear system whose coefficient matrix is an H-matrix. Fast and efficient methods of calculating componentwise error bounds of the computed solution are proposed. The methods are based on the verified criterion for an M-matrix. The main point of this article is that the proposed methods can be applied with any iterative solution methods such as the Gauss-Seidel method and Krylov subspace methods. Therefore, the sparsity of the coefficient matrix is preserved i
AbstractValidated solution of a problem means to compute error bounds for a solution in finite preci...
AbstractIn a preceding paper (Hackbusch, Computing 62 (1999) 89–108), a class of matrices (H-matrice...
We give a new theoretical tool to solve sparse systems with finitely many solutions. It is based on ...
Abstract Some new methods will be presented for computing verified inclusions of the solution of lar...
In this paper we describe verification methods for dense and large sparse systems of linear and nonl...
Abstract—This paper is concerned with the problem of verifying an accuracy of a computed solution of...
We consider the problem of approximate solution ex of a linear system Ax = b over the reals, such th...
AbstractWe consider the problem of approximate solution x̄ of of a linear system Ax = b over the rea...
AbstractIn the theory and applications of Numerical Linear Algebra the class of H-matrices is very i...
AbstractA class of parallel decomposition-type accelerated over-relaxation methods, including four a...
The mathematical models of many practical problems lead to systems of linear algebraic equations wh...
Some new methods will be presented for computing verified inclusions of the solution of large linear...
For large scale problems in electric circuit simulation as well as in chemical process simulation, t...
Abstract. In this paper, we are concerned with a matrix equation Ax = b where A is an n × n real mat...
Abstract—A fast and portable verification method is proposed for computing tight and componentwise e...
AbstractValidated solution of a problem means to compute error bounds for a solution in finite preci...
AbstractIn a preceding paper (Hackbusch, Computing 62 (1999) 89–108), a class of matrices (H-matrice...
We give a new theoretical tool to solve sparse systems with finitely many solutions. It is based on ...
Abstract Some new methods will be presented for computing verified inclusions of the solution of lar...
In this paper we describe verification methods for dense and large sparse systems of linear and nonl...
Abstract—This paper is concerned with the problem of verifying an accuracy of a computed solution of...
We consider the problem of approximate solution ex of a linear system Ax = b over the reals, such th...
AbstractWe consider the problem of approximate solution x̄ of of a linear system Ax = b over the rea...
AbstractIn the theory and applications of Numerical Linear Algebra the class of H-matrices is very i...
AbstractA class of parallel decomposition-type accelerated over-relaxation methods, including four a...
The mathematical models of many practical problems lead to systems of linear algebraic equations wh...
Some new methods will be presented for computing verified inclusions of the solution of large linear...
For large scale problems in electric circuit simulation as well as in chemical process simulation, t...
Abstract. In this paper, we are concerned with a matrix equation Ax = b where A is an n × n real mat...
Abstract—A fast and portable verification method is proposed for computing tight and componentwise e...
AbstractValidated solution of a problem means to compute error bounds for a solution in finite preci...
AbstractIn a preceding paper (Hackbusch, Computing 62 (1999) 89–108), a class of matrices (H-matrice...
We give a new theoretical tool to solve sparse systems with finitely many solutions. It is based on ...