EPSRC Reference: 
GR/R22612/01 
Title: 
Numerical Analysis of Matrix Functions 
Principal Investigator: 
Higham, Professor NJ 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematics 
Organisation: 
Victoria University of Manchester, The 
Scheme: 
Standard Research (PreFEC) 
Starts: 
01 February 2001 
Ends: 
31 January 2004 
Value (£): 
129,092

EPSRC Research Topic Classifications: 

EPSRC Industrial Sector Classifications: 
Information Technologies 
No relevance to Underpinning Sectors 

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Panel History: 

Summary on Grant Application Form 
Functions of a matrix are ubiquitous in applied mathematics. The exponential of a matrix, for example, arises explicitly or implicitly in the solution of differential equations in control theory, nuclear magentic resonance, and geometric integration. Inverse problems in these areas require the matrix logarithm. We plan to make significant advances in the theory and computation of matrix functions, paying careful attention to the needs of practitioners in applications. A major contribution will be to develop a reliable Schurbased method for computing a general function f(A), and provide software. Such a method is currently lacking, but will be of wide use and will, we believe, outperform many methods that have been suggested for specific functions. We will also develop specialized methods for the matrix exponential, other transcendental functions, and matrix p'th roots. A novel problem arising in lattice quantum chromodynamics will be investigated: how to compute f(A)b without computing f(A), when A is a large, sparse matrix. We will develop structured perturbation theory and corresponding condition numbers and combine them with rounding error analysis to understand the behaviour of our methods in floating point arithmetic.

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