Precise calculations are made of the scattering intensity I(q) from an oriented stack of lipid bilayers using a realistic model of fluctuations. The quantities of interest include the bilayer bending modulus Kc, the interbilayer interaction modulus B, and bilayer structure through the form factor F(qz). It is shown how Kc and B may be obtained from data at large q(z) where fluctuations dominate...

In this paper we demonstrate the parallelism of the spectral division via the matrix sign function for the generalized nonsymmetric eigenproblem. We employ the so-called generalized Newton iterative scheme in order to compute the sign function of a matrix pair. A recent study has allowed considerable reduction (by 75%) in the computational cost of this iteration, making this approach competitiv...

The rational QZ method generalizes the by implicitly supporting subspace iteration. In this paper we extend introducing shifts and poles of higher multiplicity in Hessenberg pencil, which is a pencil consisting two matrices. result multishift, multipole iteration on block pencils allows one to stick real arithmetic for input pencil. combination with optimally packed aggressive early deflation a...

We implement a structure-preserving numerical algorithm for extracting the eigenvectors associated to the purely imaginary eigenvalues of skew-Hamiltonian/Hamiltonian matrix pencils. We compare the new algorithm with the QZ algorithm using random examples with di erent di culty. The results show that the new algorithm is signi cantly faster, more robust, and more accurate, especially for hard e...

A fast Fortran implementation of a variant of Gragg’s unitary Hessenberg QR algorithm is presented. It is proved, moreover, that all QRand QZ-like algorithms for the unitary eigenvalue problems are equivalent. The algorithm is backward stable. Numerical experiments are presented that confirm the backward stability and compare the speed and accuracy of this algorithm with other methods.

Let S be a fixed finite symmetric subset of SLd(Z), and assume that it generates a Zariski-dense subgroup G. We show that the Cayley graphs of πq(G) with respect to the generating set πq(S) form a family of expanders, where πq is the projection map Z → Z/qZ.

A quantum algorithm for the Hidden Subgroup Problem over the group Z/pZ o Z/qZ is presented. This algorithm, which for certain parameters of the group qualifies as ‘efficient’, generalizes prior work on related semi-direct product groups. 1998 ACM Subject Classification F.1.2 Modes of Computation, F.2.2 Nonnumerical Algorithms and Problems