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For a prime power q, we study the distribution of permanents of n x n matrices over a finite field Fq of q elements. We show that if A is a sufficiently large subset of Fq, then the set of permanents of n x n matrices with entries in A covers all (or almost all) of Fq* . When q = p is a prime, and A is a subinterval of [0, p - 1] of cardinality |A| >> p1/2 log p, we show that the number of matrices with entries in A having permanent t is asymptotically close to the expected value. [ABSTRACT FROM AUTHOR]

The original TPABLO algorithms are a collection of algorithms which compute a symmetric permutation of a linear system such that the permuted system has a relatively full block diagonal with relatively large nonzero entries. This block diagonal can then be used as a preconditioner. We propose and analyze three extensions of this approach: We incorporate a nonsymmetric permutation to obtain a large diagonal, we use a more general parametrization for TPABLO, and we use a block Gauss-Seidel preconditioner which can be implemented to have the same execution time as the corresponding block Jacobi preconditioner. Experiments are presented showing that for certain classes of matrices, the block Gauss-Seidel preconditioner used with the system permuted with the new algorithm can outperform the best ILUT preconditioners in a large set of experiments. [ABSTRACT FROM AUTHOR]

We show how the Arnoldi algorithm for approximating a function of a matrix times a vector can be restarted in a manner analogous to restarted Krylov subspace methods for solving linear systems of equations. The resulting restarted algorithm reduces to other known algorithms for the reciprocal and the exponential functions. We further show that the restarted algorithm inherits the superlinear convergence property of its unrestarted counterpart for entire functions and present the results of numerical experiments. [ABSTRACT FROM AUTHOR]

We give an error estimate for the energy and helicity preserving scheme (EHPS) in second order finite difference setting on axisymmetric incompressible flows with swirling velocity. This is accomplished by a weighted energy estimate, along with careful and nonstandard local truncation error analysis near the geometric singularity and a far field decay estimate for the stream function. A key ingredient in our a priori estimate is the permutation identities associated with the Jacobians, which are also a unique feature that distinguishes EHPS from standard finite difference schemes. [ABSTRACT FROM AUTHOR]

The matrix volume is a generalization, to rectangular matrices, of the absolute value of the determinant. In particular, the matrix volume can be used in change-of-variables formulae, instead of the determinant (if the Jacobi matrix of the underlying transformation is rectangular). This result is applicable to integration on surfaces, illustrated here by several examples. [ABSTRACT FROM AUTHOR]