Accurate simple zeros of polynomials in floating point arithmetic
Computers & Mathematics with Applications
ESA'05 Proceedings of the 13th annual European conference on Algorithms
An eigenvalue search method using the Orr-Sommerfeld equation for shear flow
Journal of Computational and Applied Mathematics
Accurate evaluation of the k-th derivative of a polynomial and its application
Journal of Computational and Applied Mathematics
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We examine the behavior of Newton's method in floating point arithmetic, allowing for extended precision in computation of the residual, inaccurate evaluation of the Jacobian and unstable solution of the linear systems. We bound the limiting accuracy and the smallest norm of the residual. The application that motivates this work is iterative refinement for the generalized eigenvalue problem. We show that iterative refinement by Newton's method can be used to improve the forward and backward errors of computed eigenpairs.