Structured backward error and condition
نویسندگان
چکیده
We present a formulation for the structured condition number and for the structured backward error for the linear system A Ax = b, when the rectangular matrix A is subjected to normwise perturbations. Perturbations on the data A and the solution x are measured in the Frobenius norm. Numerical experiments that show the relevance of this condition number in the prediction of the computing error when solving such systems are provided.
منابع مشابه
On a Structured Backward Error Analysis for Linear Systems of the Type a Ax = B
The authors present a formulation for the structured condition number and bounds for the structured backward error for the linear system A Ax = b when the square matrix A is subjected to normwise perturbations. Perturbations on the data A and the solution x are measured in the Frobenius norm. Numerical experiments that show the relevance of this condition number in the prediction of the computi...
متن کاملBackward Error and Condition of Structured Linear Systems
Existing deenitions of backward error and condition number for linear systems do not cater for structure in the coeecient matrix, except possibly for sparsity. We extend the deenitions so that when the coeecient matrix has structure the perturbed matrix has this structure too. We show that when the structure comprises linear dependence on a set of parameters the structured componentwise backwar...
متن کاملNote on the backward error analysis of linear systemsof the kind A Ax = bVal
The authors derive a formulation for the structured condition number and bounds for structured backward error for the linear system A Ax = b when the square matrix A is subject to normwise perturbations. Perturbations on the data and the solution are measured in the Frobenius norm. Then numerical experiments that shows the relevance of this condition number in the prediction of the computing er...
متن کاملThe structured sensitivity of Vandermonde-like systems
We consider a general class of structured matrices that includes (possibly confluent) Vandermonde and Vandermonde-like matrices. Here the entries in the matrix depend nonlinearly upon a vector of parameters. We define condition numbers that measure the componentwise sensitivity of the associated primal and dual solutions to small componentwise perturbations in the parameters and in the right-ha...
متن کاملStructured Condition Numbers and Backward Errors in Scalar Product Spaces
We investigate the effect of structure-preserving perturbations on the solution to a linear system, matrix inversion, and distance to singularity. Particular attention is paid to linear and nonlinear structures that form Lie algebras, Jordan algebras and automorphism groups of a scalar product. These include complex symmetric, pseudo-symmetric, persymmetric, skewsymmetric, Hamiltonian, unitary,...
متن کامل