Neuberger's double-pass algorithm
Journal
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Journal Volume
68
Journal Issue
6 2
Pages
667041-667049
Date Issued
2003
Author(s)
Hsieh, T.-H.
Abstract
We analyze Neuberger's double-pass algorithm for the matrix-vector multiplication R(H) x Y [where R(H) is (n-1,n)th degree rational polynomial of positive definite operator H], and show that the number of floating-point operations is independent of the degree n, provided that the number of sites is much larger than the number of iterations in the conjugate gradient. This implies that the matrix-vector product (H)(-1/2)Y approximately R((n-1,n))(H).Y can be approximated to very high precision with sufficiently large n, without noticeably extra costs. Further, we show that there exists a threshold n(T) such that the double-pass is faster than the single pass for n>n(T), where n(T) approximately 12-25 for most platforms.
Type
journal article