EPSRC Reference: 
GR/T08739/01 
Title: 
Topics in Matrix Computations 
Principal Investigator: 
Higham, Professor NJ 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematics 
Organisation: 
University of Manchester, The 
Scheme: 
Mathematics Small Grant PreFEC 
Starts: 
01 April 2004 
Ends: 
31 August 2004 
Value (£): 
10,239

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 

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Panel History: 

Summary on Grant Application Form 
This work concerns three timely topics in matrix computations on which the investigators intend to collaborate with the proposed VF Profesor Roy Mathias (College of William and Mary, Williamsburg). We will investigate perturbation theory for, and computation of, the eigenvalues and eigenvectors of hyperbolic quadratic eigenvalue problems, for which important applications are in structural mechanics. We will develop algorithms to compute f(A)b, using only matrix vector products, and we will analyze the quality of the approximations they produce. Here A is an nxn matrix, b is an nvector and f is a function, for instance f(A) = sign(A) as arises in lattice quantum chromodynamics (QCD). We will also investigate the perturbation theory of the generalized polar decomposition A = WS, where W and S are in the automorphism group and Jordan algebra associated with a scalar product product, repectively. We wish to develop sharp bounds for the changes in W and S induced by changes in A, and hence to identify the condition numbers of W and S.

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Organisation Website: 
http://www.man.ac.uk 