Numerical solution of eigenvalue problems by means of a wavelet-based Lanczos decomposition
Patrick Fischer · International Journal of Quantum Chemistry · 2000
The simple Lanczos process is very efficient for finding a few extreme eigenvalues of a large symmetric matrix. The main task in each iteration step consists in evaluating a matrix-vector product. It is shown how to apply a fast wavelet-based product in order to speed up computations. Some numerical results are given for three different monodimensional cases: the harmonic oscillator case, the hydrogenlike atoms, and a problem with a pseudo-double-well potential. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 552–562, 2000