Addendum to: Why Gaussian quadrature in the complex plane? (English) Zbl 0993.41018

Saylor, Paul E.; Smolarski, Dennis C.

Numer. Algorithms 27, No. 2, 215-217 (2001).

This addendum clarifies that some relations, considered by the authors in a previous paper [Numer. Algorithms 26, No. 3, 251-280 (2001; Zbl 0977.41013)],refer to very general cases. More precisely, the relation between the scattering amplitude and the error in the conjugate gradient method, concerns the general case in which the matrices are non-Hermitian, whereas the conjugate gradient method assumes the matrix is Hermitian positive definite. Further, the integrals considered in the paper are over contours in the complex plane with weight functions that are not necessarily positive but could be complex valued and, if real, could take both positive and negative values.

Reviewer: Luigi Gatteschi (Torino)

MSC:

41A55	Approximate quadratures
65D30	Numerical integration
65F10	Iterative numerical methods for linear systems

Keywords:

scattering amplitude; conjugate gradient method

Software:

KELLEY