Add to ORKGAbstract — We discuss methods to compute error bounds for extremely ill-conditioned problems. As a model problem we treat matrix inversion. We demon-strate that additive corrections to improve an approx-imate inverse are useful for ill-conditioned problems, but hardly usable for extremely ill-conditioned prob-lems. Here multiplicative corrections can be used, in-cluding the possibility to compute guaranteed error bounds. 1
International audienceWe propose a general proximal algorithm for the inversion of ill-conditioned m...
In this paper, we discuss several (old and new) estimates for the norm of the error in the solution ...
Originated from the practical implementation and numerical considerations of iterative methods for s...
We consider the cost of estimating an error bound for the computed solution of a system of linear eq...
AbstractThe classical condition number is a very rough measure of the effect of perturbations on the...
In this paper we compare the performance of several methods for providing tight error bounds for lin...
In solving a system of n linear equations in d variables Ax=b, the condition number of the (n,d) m...
An accurate numerical method is established for matrix inversion. It is shown theoretically that the...
Abstract. An accurate numerical method is established for matrix inversion. It is shown theoreticall...
A problem is said to be ill-posed if the solution of the problem does not depend continuously on the...
In this paper, the problem of inverting regular matrices with arbitrarily large condi-tion number is...
This work develops a computational approach for boundary and initial-value problems by using operati...
Let IF be floating-point number system with basis beta > 2 and an exponent range consisting at least...
AbstractA problem is said to be ill-posed if the solution of the problem does not depend continuousl...
The computation of an approximate solution of linear discrete illposed problems with contaminated da...
International audienceWe propose a general proximal algorithm for the inversion of ill-conditioned m...
In this paper, we discuss several (old and new) estimates for the norm of the error in the solution ...
Originated from the practical implementation and numerical considerations of iterative methods for s...
We consider the cost of estimating an error bound for the computed solution of a system of linear eq...
AbstractThe classical condition number is a very rough measure of the effect of perturbations on the...
In this paper we compare the performance of several methods for providing tight error bounds for lin...
In solving a system of n linear equations in d variables Ax=b, the condition number of the (n,d) m...
An accurate numerical method is established for matrix inversion. It is shown theoretically that the...
Abstract. An accurate numerical method is established for matrix inversion. It is shown theoreticall...
A problem is said to be ill-posed if the solution of the problem does not depend continuously on the...
In this paper, the problem of inverting regular matrices with arbitrarily large condi-tion number is...
This work develops a computational approach for boundary and initial-value problems by using operati...
Let IF be floating-point number system with basis beta > 2 and an exponent range consisting at least...
AbstractA problem is said to be ill-posed if the solution of the problem does not depend continuousl...
The computation of an approximate solution of linear discrete illposed problems with contaminated da...
International audienceWe propose a general proximal algorithm for the inversion of ill-conditioned m...
In this paper, we discuss several (old and new) estimates for the norm of the error in the solution ...
Originated from the practical implementation and numerical considerations of iterative methods for s...