Numerical Algorithms

Applying the generalized Euler transform to the firstn partial sums of a power series results in a triangular array whose inferior diagonal givesn approximate values of the sum of this series. The aim of this short note is to estimate the best of thesen ...

This is the second part of a note on interpolation by real polynomials of several real variables. For certain regular knot systems (geometric or regular meshes, tensor product grids), Neville-Aitken algorithms are derived explicitly. By application of a ...

In a recent paper Chan and Chan study the use of circulant preconditioners for the solution of elliptic problems. They prove that circulant preconditioners can be chosen so that the condition number of the preconditioned system can be reduced from O(n ...

We consider a dilation operator T admitting a scaling function with compact support as fixed point. It is shown that the adjoint operator T* admits a sequence of polynomial eigenfunctions and that a smooth function f admits an expansion in these ...

In this paper a new algorithm for solving special Vandermonde systems is presented, useful when then points defining the matrix are thek th roots ofm complex numbers (n=km); if they are real and positive andn=2m, the usual case of real points ...

For boundary value problems posed on unbounded domains it is often appropriate to impose a boundary condition at "infinity". For certain classes of boundary value problem obvious numerical difficulties can be avoided by truncating the unbounded domain ...

A class of polyhedral norms is introduced, which contains the l ₁ and l norms as special cases. Of primary interest is the solution of linear best approximation problems using these norms. Best approximations are characterized, and an algorithm is ...

Numerical methods for ordinary initial value problems that do not depend on special properties of the system are usually found in the class of linear multistage multivalue methods, first formulated by J.C. Butcher. Among these the explicit methods are ...

Stability analysis of Runge-Kutta (RK) formulas was originally limited to linear ordinary differential equations (ODEs). More recently such analysis has been extended to include the behaviour of solutions to nonlinear problems. This extension led to ...

We present a block algorithm for computing rank-revealing QR factorizations (RRQR factorizations) of rank-deficient matrices. The algorithm is a block generalization of the RRQR-algorithm of Foster and Chan. While the unblocked algorithm reveals the ...

A convergence acceleration result for the E-algorithm is proved for sequences such that the error has an asymptotic expansion on a scale of comparison for which a determinantal relation holds. This result is also generalized to the vector case.

It is shown how the combined discretization and cutting plane method for general convex semi-infinite programming problems recently presented in [40] can be effectively implemented for the solution of minimax problems in the complex plane. In contrast ...