The Lanczos optimization of a splitting-up method to solve homogeneous evolutionary equations (Q1200188)

In classical schemes of solving symmetric systems of homogeneous ordinary differential equations the number of matrix-vector operations with the finite difference matrix is proportional to the number of time steps. It is shown that the Lanczos method provides the \(\sqrt s\) advantage. This technique is used for solving the two-dimensional heat condition equation. It is noted that the arithmetical costs are reduced by a factor of 3 up to 60 in comparison to the classical approach. The combination of a splitting scheme and the Lanczos method may be used with advantage for the lower part of the spectrum.