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Iterative Methods for the Solution of Equations
General Preliminaries: 1.1 Introduction 1.2 Basic concepts and notations General Theorems on Iteration Functions: 2.1 The solution of a fixed-point problem 2.2 Linear and superlinear convergence 2.3Expand
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Optimal Order of One-Point and Multipoint Iteration
TLDR
The problem is to calculate a simple zero of a nonlinear function ƒ by iteration. Expand
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A general theory of optimal algorithms
TLDR
By reading, you can know the knowledge and things more, not only about what you get from people to people. Expand
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Information-based complexity
TLDR
Information-based complexity seeks to develop general results about the intrinsic difficulty of solving problems where available information is partial or approximate and to apply these results to specific problems. Expand
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Faster Valuation of Financial Derivatives
TLDR
We report on numerical testing which compares low-discrepancy and Monte Carlo algorithms on the evaluation of financial derivatives which is formulated as the computation of ten integrals of dimension up to 360. Expand
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On Euclid's Algorithm and the Theory of Subresultants
TLDR
This paper presents an elementary treatment of the theory of subresultants, and examines the relationship of the sub resultants of a given pair of polynomials to their polynomial remainder sequence as determined by Euclid's algorithm. Expand
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Convergence and Complexity of Newton Iteration for Operator Equations
TLDR
An optimal convergence condition for Newton iteration in a Banach space is established. Expand
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A three-stage variable-shift iteration for polynomial zeros and its relation to generalized rayleigh iteration
SummaryWe introduce a new three-stage process for calculating the zeros of a polynomial with complex coefficients. The algorithm is similar in spirit to the two stage algorithms studied by Traub in aExpand
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Complexity and information
Part I. Fundamentals: 1. Introduction 2. Information-based complexity 3. Breaking the curse of dimensionality Part II. Some Interesting Topics: 4. Very high-dimensional integration and mathematicalExpand
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The Algebraic Theory of Matrix Polynomials
A matrix S is a solvent of the matrix polynomial $M(X) = A_0 X^m + \cdots + A_m $ if $M(S) = 0$ where $A_i ,X,S$ are square matrices. In this paper we develop the algebraic theory of matrixExpand
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