Add to ORKGAbstract. Validated solution of a problem means to compute error bounds for a solution in finite precision. This includes the proof of existence of a solution. The computed error bounds are to be correct including all possible effects of rounding errors. The fastest known validation algorithm for the solution of a system of linear equations requires twice the computing time of a standard (purely) numerical algorithm. In this paper we present a super-fast validation algorithm for linear systems with symmetric positive definite matrix. This means that the entire computing time for the validation algorithm including computation of an approximated solution is the same as for a standard numerical algorithm. Numerical results are presented. 1. In...
Abstract—A fast and portable verification method is proposed for computing tight and componentwise e...
International audienceA symbolic-numeric validation algorithm is developed to compute rigorous and t...
Abstract. In this paper, we are concerned with a matrix equation Ax = b where A is an n × n real mat...
AbstractValidated solution of a problem means to compute error bounds for a solution in finite preci...
International audienceSolving numerically a linear system can be performed very efficiently, using o...
Abstract. In this paper we describe some of the principles of methods for the verified solution of l...
International audienceThe problem considered in this talk is to solve and mainly to refine an approx...
Interval arithmetic is a means to compute verified results. However, a naive use of interval arithme...
Abstract. We present a computational, simple and fast sufficient criterion to verify positive defini...
Some new methods will be presented for computing verified inclusions of the solution of large linear...
A parallel version of the self-verified method for solving linear systems was presented on PARA and ...
What is the fastest way to solve a linear system $Ax= b$ in arithmetic of a given precision when $A$...
This paper is concerned with the problem of verifying the accuracy of an approximate solution of a s...
summary:This paper concerns accuracy-guaranteed numerical computations for linear systems. Due to th...
We review some of the most important results in the area of fast parallel algorithms for the solutio...
Abstract—A fast and portable verification method is proposed for computing tight and componentwise e...
International audienceA symbolic-numeric validation algorithm is developed to compute rigorous and t...
Abstract. In this paper, we are concerned with a matrix equation Ax = b where A is an n × n real mat...
AbstractValidated solution of a problem means to compute error bounds for a solution in finite preci...
International audienceSolving numerically a linear system can be performed very efficiently, using o...
Abstract. In this paper we describe some of the principles of methods for the verified solution of l...
International audienceThe problem considered in this talk is to solve and mainly to refine an approx...
Interval arithmetic is a means to compute verified results. However, a naive use of interval arithme...
Abstract. We present a computational, simple and fast sufficient criterion to verify positive defini...
Some new methods will be presented for computing verified inclusions of the solution of large linear...
A parallel version of the self-verified method for solving linear systems was presented on PARA and ...
What is the fastest way to solve a linear system $Ax= b$ in arithmetic of a given precision when $A$...
This paper is concerned with the problem of verifying the accuracy of an approximate solution of a s...
summary:This paper concerns accuracy-guaranteed numerical computations for linear systems. Due to th...
We review some of the most important results in the area of fast parallel algorithms for the solutio...
Abstract—A fast and portable verification method is proposed for computing tight and componentwise e...
International audienceA symbolic-numeric validation algorithm is developed to compute rigorous and t...
Abstract. In this paper, we are concerned with a matrix equation Ax = b where A is an n × n real mat...