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The algebraic eigenvalue problem
Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices ofExpand
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Rounding errors in algebraic processes
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Error Analysis of Direct Methods of Matrix Inversion
TLDR
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
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Inverse Iteration, Ill-Conditioned Equations and Newton’s Method
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: aExpand
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AN ESTIMATE FOR THE CONDITION NUMBER OF A MATRIX
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
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Note on matrices with a very ill-conditioned eigenproblem
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 publishedExpand
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The Least Squares Problem and Pseudo-Inverses
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Error analysis of floating-point computation
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 areExpand
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Ill-conditioned eigensystems and the computation of the Jordan canonical form
TLDR
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
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