Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of… Expand

We analyze the effect of the rounding errors made in the solution of the problem of inverting a matrix using vector and matr ix norms for a number of direct methods.Expand

Inverse iteration is one of the most widely used algorithms in practical linear algebra but an understanding of its main numerical properties has developed piecemeal over the last thirty years: a… Expand

It is important in practice when solving linear systems to have an economical method for estimating the condition number $\kappa (A)$ of the matrix of coefficients. An algorithm involving $O(n^2 )$… Expand

SummaryGives a bound for the distance of a matrix having an ill-conditioned eigenvalue problem from a matrix having a multiple eigenvalue which is generally sharper than that which has been published… Expand

This paper consists of two main sections. In the first the bounds are derived for the rounding errors made in the fundamental floating-point arithmetic operations. In the second, these results are… Expand

The solution of the complete eigenvalue problem for a non-normal matrix A presents severe practical difficulties when A is defective or close to a defective matrix.Expand