ylfink@water.waterloo.edu (ylfink) (04/13/88)
DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF WATERLOO SEMINAR ACTIVITIES SYMBOLIC COMPUTATION SEMINAR - Thursday, April 14, 1988 Dr. George Labahn, from the University of Alberta, will speak on ``Matrix Pade Forms and Inverses of Block Hankel Matrices''. TIME: 3:30 PM ROOM: MC 6082 ABSTRACT Systems of equations where the coefficient matrix has the structure of a block Hankel (or block Toeplitz) matrix appear in many diverse branches of mathematics and engineering. They are used, for example, in signal processing and image processing (to calculate digital filters), in algebraic computation (to calculate GCD's of polynomials), and also in the determination of rational approximants (matrix Pade forms) of a power series. In this talk we solve such systems by taking advantage of the relationship between block Hankel matrices and matrix Pade forms. An algorithm, MPADE, is given that calculates matrix Pade forms of any type. This algorithm also provides for an easy mechanism to decide on the invertibility of the coefficient block Hankel for our system. In the case where the matrix is indeed invertible we present a set of closed inverse formulae that are given in terms of the matrix Pade forms calculated by MPADE. Thus we determine the inverse and solve the system. This approach allows for significant advantages in reliability, storage and efficiency over existing methods. Directions for future research along with interesting side-effects of our work will also be presented.