Implementation of a variable block Davidson method with deflation for solving large sparse eigenproblems

The Davidson method is a preconditioned eigenvalue technique aimed at computing a few of the extreme (i.e., leftmost or rightmost) eigenpairs of large sparse symmetric matrices. This paper describes a software package which implements a deflated and variable-block version of the Davidson method. Information on how to use the software is provided. Guidelines for its upgrading or for its incorporation into existing packages are also included. Various experiments are performed on an SGI Power Challenge and comparisons with ARPACK are reported. This revised version was published online in June 2006 with corrections to the Cover Date.     

Stability number and [a,b]‐factors in graphs

A spanning subgraph whose vertices have degrees belonging to the interval [a,b], where a and b are positive integers, such that a ≤ b, is called an [a,b]‐factor. In this paper, we prove sufficient conditions for existence of an [a,b]‐factor, a connected [a,b]‐factor, and a 2‐connected [a,b]‐factor. The conditions involve the minimum degree, the stability number, and the connectivity of a graph. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 254–264, 2004     

ChebStaBlkCG: A block variant of ChebFilterCG

The behavior of ChebFilterCG (an algorithm that combines the Chebyshev filter and Conjugate Gradient) applied to systems with unfavorable eigenvalue distribution is examined. To improve the convergence, a hybrid approach combining a stabilized version of the block conjugated gradient with Chebyshev polynomials as preconditioners (ChebStaBlkCG) is proposed. The performance of ChebStaBlkCG is illustrated and validated on a set of linear systems. It is shown how ChebStaBlkCG can be used to accelerate the block Cimmino method and to solve linear systems with multiple right‐hand sides.     

On the squared Smith method for large‐scale Stein equations

A squared Smith type algorithm for solving large‐scale discrete‐time Stein equations is developed. The algorithm uses restarted Krylov spaces to compute approximations of the squared Smith iterations in low‐rank factored form. Fast convergence results when very few iterations of the alternating direction implicit method are applied to the Stein equation beforehand. The convergence of the algorithm is discussed and its performance is demonstrated by several test examples. Copyright © 2013 John Wiley & Sons, Ltd.     

Bounds for the b-chromatic number of some families of graphs

In this paper we obtain some upper bounds for the b-chromatic number of K_1,s-free graphs, graphs with given minimum clique partition and bipartite graphs. These bounds are given in terms of either the clique number or the chromatic number of a graph or the biclique number for a bipartite graph. We show that all the bounds are tight.     

Strange baryon production in heavy ion collisions

The rapidity distribution of Λ and ?Λ produced in nucleus-nucleus collisions at CERN energies is studied in the framework of an independent string model — with quark-antiquark as well as diquark-antidiquark pairs in the nucleon sea. It is shown that, besides the Λ-?Λ pair production resulting from the fragmentation of sea diquarks, final state interactions of co-moving secondaries π + N → K + Λ and ?N → K → ?Λ are needed in order to reproduce the data. Predictions for Pb-Pb collisions are presented.     

Block-Arnoldi and Davidson methods for unsymmetric large eigenvalue problems

Summary We present two methods for computing the leading eigenpairs of large sparse unsymmetric matrices. Namely the block-Arnoldi method and an adaptation of the Davidson method to unsymmetric matrices. We give some theoretical results concerning the convergence and discuss implementation aspects of the two methods. Finally some results of numerical tests on a variety of matrices, in which we compare these two methods are reported.     

Influence of physical parameters and lubricants on the compaction properties of granulated and non-granulated cross-linked high amylose starch

Cross-linked high amylose starch (CLA) is a pharmaceutical excipient used in direct compression for the preparation of controlled release tablets and implants. In this work the compression properties of CLA in bulk and granulated forms (without binder) were evaluated for the first time. Tablets were prepared on an instrumented single punch machine. The flow properties and the compression characteristics (compressibility, densification behavior, work of compression) of the materials as well as the mechanical strength of the finished compacts (compactibility) were systematically examined. Wet granulation was found to improve the flowability and the compressibility of CLA but concomitantly reduced its compactibility. It was demonstrated that CLA was a plastically deforming material with a plasticity index and a yield pressure value comparable to those of pregelatinized starch. The compactibility of granulated CLA was independent of particle size in the range of 75 to 500 microm, but slightly decreased when the percentage of the fine particles (<75 microm) in the bulk powder was increased. Water and colloidal silicone dioxide facilitated the consolidation of CLA, while magnesium stearate had an opposite effect on the tablet crushing force.