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 2.3… Expand

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

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

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

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 a… Expand

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 mathematical… Expand

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 matrix… Expand