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A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions
This paper gives a method for finding sharp a posteriori error bounds for Newton's method under the assumptions of Kantorovich's theorem. On the basis...
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Error Bounds for Newton’s Method Under the Kantorovich Assumptions
A principle which finds sharp a posteriori error bounds for Newton’s method is given under the assumptions of Kantorovich’s theorem. On the basis of...
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Error analysis of an algorithm for solving an underdetermined linear system
The accumulation of rounding errors in a method used to compute the solution of an underdetermined system of linear equations at the least distance...
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On the stability of a class of convergence acceleration methods for power series
In this paper we study the problem of evaluating the sum of a power series whose terms are given numerically with a moderate accuracy. For a large...
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Singularly perturbed finite element methods
This paper introduces a new piecewise linear finite element, which is designed to handle singularly perturbed ordinary differential equations. Both...
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An error analysis for the secant method
Sharp a priori and a posteriori error bounds are given for the secant method for solving non-linear equations in Banach spaces. The numerical...