Compact C language Fourier analysis on small computers

Fourier Integral Operators and Harmonic Analysis On Compact Manifolds

Compact Fourier Analysis for Multigrid Methods based on Block Symbols

The notion of Compact Fourier Analysis (CFA) is discussed. The CFA allows description of multigrid (MG) in a nutshell and offers a clear overview on all MG components. The principal idea of CFA is to model the MG mechanisms by means of scalar generating functions and matrix functions (block symbols). The formalism of the CFA approach is presented by describing the symbols of the fine and coarse...

Compact Fourier Analysis for Designing Multigrid Methods

The convergence of Multigrid methods can be analyzed based on a Fourier analysis of the method or by proving certain inequalities that have to be fulfilled by the smoother and by the coarse grid correction separately. Here, we analyze the Multigrid method for the constant coefficient Poisson equation with a compact Fourier analysis using the formalism of multilevel Toeplitz matrices and their g...

A Procedure for Implementing the Fast Fourier Transform on Small Computers

A technique has been developed that adapts the Fast Fourier Transform algorithm for implementation on computers having relatively long multiplication times. The technique is particularly well suited to real-time processing on a small data acquisition computer such as the IBM System/7. Four basic ideas are utilized to improve the performance of the original Cooley-Tukey algorithm on such a machi...

Lattice QCD on Small Computers

We demonstrate that lattice QCD calculations can be made 103– 10 times faster by using very coarse lattices. To obtain accurate results, we replace the standard lattice actions by perturbativelyimproved actions with tadpole-improved correction terms that remove the leading errors due to the lattice. To illustrate the power of this approach, we calculate the static-quark potential, and the charm...