Block Lanczos algorithm

The block Lanczos algorithm finds the nullspace of a matrix over a finite field, using only multiplications of the matrix by long, thin matrices. Those thin matrices are treated as vectors whose entries are tuples of finite-field elements, which is why descriptions of the method call them vectors. It is among the most efficient known ways to compute nullspaces, the final stage of integer factorization methods such as the quadratic sieve and the number field sieve, and its development has been driven almost entirely by that use. It is based on the Lanczos algorithm for eigenvalues of large sparse real matrices. It is hard to parallelize across machines, because the whole vector must be available at the end of each iteration, so the block Wiedemann algorithm suits clusters of independent systems better.