AbstractWe study an average condition number and an average loss of precision for the solution of linear equations and prove that the average case is strongly related to the worst case. This holds if the perturbations of the matrix are measured in Frobenius or spectral norm or componentwise. In particular, for the Frobenius norm we show that one gains about log2n+0.9 bits on the average as compared to the worst case, n being the dimension of the system of linear equations
AbstractIn this note we generalize an upper bound given in Guggenheimer et al. (College Math. J. 26(...
A perturbation result concerning the upper and lower bounds on relative errors of solutions to linea...
We explore the condition numbers of the nonlinear matrix equation Xp-A⁎eXA=I. Explicit expressions f...
AbstractWe study an average condition number and an average loss of precision for the solution of li...
International audienceIn this paper we are interested in computing linear least squares (LLS) condit...
Various normwise relative condition numbers that measure the sensitivity of matrix inversion and the...
The solution of a system of linear non-homogeneous equations may contain errors which originate from...
AbstractInequalities between some norms of rectangular matrices and the corresponding relationships ...
In this paper, we address the accuracy of the results for the overdetermined full rank linear least ...
We consider the cost of estimating an error bound for the computed solution of a system of linear eq...
In solving a system of n linear equations in d variables Ax=b, the condition number of the (n,d) m...
In this paper, we address the accuracy of the results for the overdetermined full rank linear least ...
This thesis examines methods to estimate errors of calculated solutions of linear systems. These met...
Several properties of matrix norms and condition numbers are described. The sharpness of the norm bo...
AbstractA perturbation result concerning the upper and lower bounds on relative errors of solutions ...
AbstractIn this note we generalize an upper bound given in Guggenheimer et al. (College Math. J. 26(...
A perturbation result concerning the upper and lower bounds on relative errors of solutions to linea...
We explore the condition numbers of the nonlinear matrix equation Xp-A⁎eXA=I. Explicit expressions f...
AbstractWe study an average condition number and an average loss of precision for the solution of li...
International audienceIn this paper we are interested in computing linear least squares (LLS) condit...
Various normwise relative condition numbers that measure the sensitivity of matrix inversion and the...
The solution of a system of linear non-homogeneous equations may contain errors which originate from...
AbstractInequalities between some norms of rectangular matrices and the corresponding relationships ...
In this paper, we address the accuracy of the results for the overdetermined full rank linear least ...
We consider the cost of estimating an error bound for the computed solution of a system of linear eq...
In solving a system of n linear equations in d variables Ax=b, the condition number of the (n,d) m...
In this paper, we address the accuracy of the results for the overdetermined full rank linear least ...
This thesis examines methods to estimate errors of calculated solutions of linear systems. These met...
Several properties of matrix norms and condition numbers are described. The sharpness of the norm bo...
AbstractA perturbation result concerning the upper and lower bounds on relative errors of solutions ...
AbstractIn this note we generalize an upper bound given in Guggenheimer et al. (College Math. J. 26(...
A perturbation result concerning the upper and lower bounds on relative errors of solutions to linea...
We explore the condition numbers of the nonlinear matrix equation Xp-A⁎eXA=I. Explicit expressions f...