Sparse Matrices and the Lanczos Algorithm

None of the above diagonalisation procedures make any use of sparsity. A very useful algorithm for tridiagonalising a sparse matrix is the Lanczos algorithm. This algorithm was developed into a very useful tool by the Cambridge group of Volker Heine (including (e.g.) Roger Haydock, Mike Kelly, John Pendry) in the late 60's and early 70's. A suite of programs based on the Lanczos algorithm can be obtained by anonymous ftp from the HENSA archive.