Recently, several experimental studies have been conducted on block data layout in conjunction with tiling as a data transformation technique to improve cache performance. In this paper, we analyze cache and TLB performance of such alternate layouts (including block data layout and Morton layout) when used in conjunction with tiling. We derive a tight lower bound on TLB performance for standard...

Two-level parallelization is introduced to solve a massive block-tridiagonal matrix system. One-level is used for distributing blocks whose size is as large as the number of block rows due to the spectral basis, and the other level is used for parallelizing in the block row dimension. The purpose of the added parallelization dimension is to retard the saturation of the scaling due to communicat...

It is shown that if the decoherence matrix corresponding to a qubit master equation has a block-diagonal real part, then the evolution is determined by a one-dimensional oscillator equation. Further, when the decoherence matrix itself is block-diagonal, then the necessary and sufficient conditions for completely positive evolution may be formulated in terms of the oscillator Hamiltonian or Lagr...

Two types of rod-coil block copolymers including poly(3-hexylthiophene)-block-poly(ethylene glycol) (P3HT-b-PEG) and PEG-block-polyaniline (PANI) were synthesized using Grignard metathesis polymerization, Suzuki coupling, and interfacial polymerization. Afterward, two types of single crystals were grown by self-seeding methodology to investigate the coily and rod blocks in grafted brushes and o...

We start by introducing a new class of structured matrix polynomials, namely, the class of MA-structured matrix polynomials, to provide a common framework for many classes of structured matrix polynomials that are important in applications: the classes of (skew-)symmetric, (anti-)palindromic, and alternating matrix polynomials. Then, we introduce the families of MAstructured strong block minima...

Matrix multiplication is a key primitive in block matrix algorithms such as those found in LAPACK. We present results from our study of matrix multiplication algorithms on the Intel Touchstone Delta, a distributed memory message-passing architecture with a two-dimensional mesh topology. We obtain an implementation that uses communications primitives highly suited to the Delta and exploits the s...

Abstract: The block-tridiagonal matrix structure is a common feature in Hamiltonians of models of transport. By allowing for a complex Bloch parameter in the boundary conditions, the Hamiltonian matrix and its transfer matrix are related by a spectral duality. As a consequence, I derive the distribution of the exponents of the transfer matrix in terms of the spectral density of the non-Hermitia...

Jacobi-Davidson methods can efficiently compute a few eigenpairs of a large sparse matrix. Block variants of JacobiDavidson are known to be more robust than the standard algorithm, but they are usually avoided as the total number of floating point operations increases. We present the implementation of a block Jacobi-Davidson solver and show by detailed performance engineering and numerical expe...

In the context of the block Cimmino algorithm, we study preprocessing strategies to obtain block partitionings that can be applied to general linear systems of equations Ax = b. We study strategies that transform the matrix AA into a matrix with a block tridiagonal structure. This provides a partitioning of the linear system for row projection methods because block Cimmino is essentially equiva...

We report for the first time exact ground-states deduced for the D = 2 dimensional generic periodic Anderson model at finite U , the Hamiltonian of the model not containing direct hopping terms for f -electrons (t = 0). The deduced itinerant phase presents non-Fermi liquid properties in the normal phase, emerges for real hybridization matrix elements, and not requires anisotropic unit cell. In ...