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Advances in Computational Mathematics Volume 6 Issue 1

Subject Areas: Applied Mathematics;
Publisher: Baltzer Science Publishers, Baarn/Kluwer Academic Publishers - Springer Journals
ISSN: 1019-7168
SJR: 60

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Preface

Twizell, E.

2005 Advances in Computational Mathematics

doi:10.1007/BF02127691
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Foreword

Howlett, Jack; Newby, J.

2005 Advances in Computational Mathematics

doi:10.1007/BF02127692
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Iterative methods for solvingAx=b, GMRES/FOM versus QMR/BiCG

Cullum, Jane

2005 Advances in Computational Mathematics

doi:10.1007/BF02127693

We study the convergence of the GMRES/FOM and QMR/BiCG methods for solving nonsymmetric systems of equationsAx=b. We prove, in exact arithmetic, that any type of residual norm convergence obtained using BiCG can also be obtained using FOM but on a different system of equations. We consider...
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Bivariate segment approximation and splines

Meinardus, G.; Nürnberger, G.; Walz, G.

2005 Advances in Computational Mathematics

doi:10.1007/BF02127694

The problem to determine partitions of a given rectangle which are optimal for segment approximation (e.g., by bivariate piecewise polynomials) is investigated. We give criteria for optimal partitions and develop algorithms for computing optimal partitions of certain types. It is shown that there...
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Numerical solution of cauchy-type integral equations of index −1 by collocation methods

Cuminato, Jose

2005 Advances in Computational Mathematics

doi:10.1007/BF02127695

This paper describes a collocation method for solving constant coefficient Cauchy-type singular integral equations of index −1. A technique for reducing the set of linear equations resulting from collocation to match the number of unknows is described. The uniform convergence analysis of the...
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A collocation method for singularly perturbed two-point boundary value problems with splines in tension

Marušić, Miljenko; Rogina, Mladen

2005 Advances in Computational Mathematics

doi:10.1007/BF02127696

An error bound for the collocation method by spline in tension is developed for a nonlinear boundary value problemay″+by′+cy=f(·,y),y(0)=y 0,y(1)=y 1. Sharp error bounds for the interpolating splines in tension are used in conjunction with recently obtained formulae for B-splines, to develop an...
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Complexity reduction of least squares problems involving special vandermonde matrices

Tommasini, T.

2005 Advances in Computational Mathematics

doi:10.1007/BF02127697

This paper presents a new QRD factorization of a rectangular Vandermonde matrix for a special point distribution, including the symmetric case, based on ak-dimensional block decomposition of the matrix and some properties of the Kronecker product. The computational reduction factor with respect...
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Interpolation regions for convex cubic curve segments

Peters, Jörg

2005 Advances in Computational Mathematics

doi:10.1007/BF02127698

Given a family of planar, convex, cubic curve segments with fixed end points and tangents, subregions of the plane are characterized in which additional points can be interpolated by at least one member of the family. The region for a second additional point is a remarkably thin double crescent.
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Barycentric coordinates for convex polytopes

Warren, Joe

2005 Advances in Computational Mathematics

doi:10.1007/BF02127699

An extension of the standard barycentric coordinate functions for simplices to arbitrary convex polytopes is described. The key to this extension is the construction, for a given convex polytope, of a unique polynomial associated with that polytope. This polynomial, theadjoint of the polytope,...
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A finite element method for interface problems in domains with smooth boundaries and interfaces

Bramble, James; King, J.

2005 Advances in Computational Mathematics

doi:10.1007/BF02127700

This paper is concerned with the analysis of a finite element method for nonhomogeneous second order elliptic interface problems on smooth domains. The method consists in approximating the domains by polygonal domains, transferring the boundary data in a natural way, and then applying a finite...

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