Addendum to: Why Gaussian Quadrature in the Complex Plane?
Response or Comment
The primary purpose of this Addendum is to clarify the relation between the scattering amplitude and the error in the conjugate gradient method (CG). Our paper concerns the more general case in which matrices are non-Hermitian, whereas CG, as is well known, assumes that the matrix is Hermitian positive definite (HPD). Note that if A is real, HPD reduces to symmetric positive definite. Also, the integrals that arise in CG are over intervals of real numbers with positive weight functions, whereas in our paper, integrals 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 on both positive and negative values.
Saylor, P. E., & Smolarski, D. C. (2001). Addendum to: Why Gaussian Quadrature in the Complex Plane? Numerical Algorithms, 27(2), 215–217. https://doi.org/10.1023/A:1011829601115