On rank and null space computation of the generalized Sylvester matrix

Abstract  In this paper, we present new approaches computing the rank and the null space of the (m
n + p)×(n + p) generalized Sylvester matrix of (m + 1) polynomials of maximal degrees n,p. We introduce an algorithm which handles directly a modification of the generalized Sylvester matrix, computing efficiently
its rank and null space and replacing n by log
₂
n in the required complexity of the classical methods. We propose also a modification of the Gauss-Jordan factorization method
applied to the appropriately modified Sylvester matrix of two polynomials for computing simultaneously its rank and null space.
The methods can work numerically and symbolically as well and are compared in respect of their error analysis, complexity
and efficiency. Applications where the computation of the null space of the generalized Sylvester matrix is required, are
also given.

• Content Type Journal Article
• Category Original Paper
• DOI 10.1007/s11075-009-9336-6
• Authors
  
  
  • Dimitrios Triantafyllou, University of Athens Department of Mathematics Panepistemiopolis 15784 Athens Greece
  • Marilena Mitrouli, University of Athens Department of Mathematics Panepistemiopolis 15784 Athens Greece
  
  

• Journal Numerical Algorithms
• Online ISSN 1572-9265
• Print ISSN 1017-1398

Published by

Original source : http://www.springerlink.com/content/y451652545w423...

Hierarchical Matrices in Computations of Electron Dynamics

Abstract  We discuss the approximation of the meanfield terms appearing in computations of the multi-configuration time-dependent Hartree–Fock
method for the solution of the time-dependent multi-particle (electronic) Schrödinger equation by hierarchical matrices. We
give theoretical error bounds for the cross approximation defined by low rank approximations of admissible matrix sub-blocks, and illustrate the gain in performance by numerical experiments.

• Content Type Journal Article
• DOI 10.1007/s10915-009-9330-0
• Authors
  
  
  • Othmar Koch, Vienna University of Technology Institute for Analysis and Scientific Computing (E101) Wiedner Hauptstraße 8–10 1040 Vienna Austria
  • Christopher Ede, Vienna University of Technology Photonics Institute (E387) Gußhausstraße 27 1040 Vienna Austria
  • Gerald Jordan, Vienna University of Technology Photonics Institute (E387) Gußhausstraße 27 1040 Vienna Austria
  • Armin Scrinzi, Vienna University of Technology Photonics Institute (E387) Gußhausstraße 27 1040 Vienna Austria
  
  

• Journal Journal of Scientific Computing
• Online ISSN 1573-7691
• Print ISSN 0885-7474

Published by

Original source : http://www.springerlink.com/content/r3p37r20657378...