This report is devoted to the proof of the global convergence and asymptotic quadratic convergence of the serial and parallel two-sided block-Jacobi SVD algorithm. In the serial case, one pair of the off-diagonal blocks with the largest weight given as the sum of squares of Frobenius norms is annihilated. In the parallel case, using the greedy implementation of dynamic ordering and having p pro...

Experience shows that there is a strong parallel between metrization theory for compact spaces and for linearly ordered spaces in terms of diagonal conditions. Recent theorems of Gruenhage, Pelant, Kombarov, and Stepanova have described metrizability of compact (and related) spaces in terms of the offdiagonal behavior of those spaces, i.e., in terms of properties of X −∆. In this paper, we show...

The q; t-Macdonald polynomials are conjectured by Garsia and Haiman to have a representation theoretic interpretation in terms of the Sn-module M spanned by the derivatives of a certain polynomial (x1; x2; : : : ; xn; y1; y2; : : : ; yn). The diagonal action of a permutation 2 Sn on a polynomial P = P (x1; x2; : : : ; xn; y1; y2; : : : ; yn) is de ned by setting P = P (x 1 ; x 2 ; : : : ; x n; ...