Eberly, Wayne2014-07-152014-07-152014-07-15http://hdl.handle.net/1880/50165Block Hankel matrices, generated according to a particular distribution, arise in the analysis of Block Wiedemann and Block Lanczos algorithms. It is shown that if the input matrix A has entries in a small finite field Fq and satisfies a condition that holds generically, then the expected nullities of these matrices are low — as needed to establish the efficiency and reliability of these algorithms. A sparse matrix preconditioner, that ensures that the above-mentioned condition holds with high probability, is also contributed.engAlgorithmsPerformanceReliabilityTheoryBlack box matrix computations, lookahead in biconditional Lanczos algorithms, early termination in Wiedemann algorithms, randomized algorithms, computations over finite fieldstechnical report2014-1060-1110.11575/PRISM/30587