SuiteSparseQR is a sparse QR factorization package based on the multifrontal method. Within each frontal matrix, LAPACK and the multithreaded BLAS enable the method to obtain high performance on multicore architectures. Parallelism across different frontal matrices is handled with Intel’s Threading Building Blocks library. The symbolic analysis and ordering phase preeliminates singletons by per...

In this work we compare semi-discrete formulations to obtain numerical solutions for the 1D Burgers equation. The formulations consist in the discretization of the time-domain via multi-stage methods of second and fourth order: R11 and R22 Padé approximants, and of the spatial-domain via finite element methods: least-squares (MEFMQ), Galerkin (MEFG) and Streamline-Upwind Petrov-Galerkin (SUPG)....

The dynamic response of polar nanoregions under an AC electric field was investigated by measuring the frequency dependence of the quadratic electro-optic (QEO) effect in a paraelectric KTa0.61Nb0.39O3 single crystal near the para-ferroelectric phase boundary (0 °C < T-Tc < 13 °C). The QEO coefficient R11 - R12 reached values as large as 5.96 × 10(-15) m(2)/V(2) at low frequency (500 Hz) and gr...

Alastair McFarlane U.S. Department of Housing and Urban Development Office of Policy Development and Research Washington, D.C. 20410 Tel. 202 708 0426 Fax 202 708 1159 Email: [email protected] Original: May 1999 First revision: August 2001 JEL Classifications: R11 (Analysis of growth, development, and changes;) R33 (Housing supply and markets); and R38 (government policies; regulatory ...

Let rk(n) denote the number of representations of an integer n as a sum of k squares. We prove that for odd primes p, r11(p) = 330 31 (p + 1) − 22(−1)(p−1)/2p4 + 352 31 H(p), where H(p) is the coefficient of q in the expansion of