Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2003-06-20
Phys.Rev.E68:066704,2003
Physics
High Energy Physics
High Energy Physics - Lattice
18 pages, v3: CPU time formulas are obtained, to appear in Physical Review E
Scientific paper
10.1103/PhysRevE.68.066704
We analyze Neuberger's double pass algorithm for the matrix-vector multiplication R(H).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 \simeq R^{(n-1,n)}(H) \cdot 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 \simeq 12 - 25 $ for most platforms.
Chiu Ting-Wai
Hsieh Tung-Han
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