Applied Mathematics Seminar

Speaker: Wayne M. Lawton (Mahidol University, Thailand)

Title: Matrices and Recursive Algorithms

Abstract: The Euclidean algorithm of antiquity proceeds by recursively multiplying a column vector \([a1 b1]^T\) , with \(a1 < b1\), on the left by a 2 x 2 matrix to give \([a2 b2=a1]^T\) where \(a2\) is the remainder of \(b1\) upon division by \(a1\). This algorithm terminates when \(an = 0\) and then \(bn\) is the greatest common divisor of \(a1\) and \(b1\). The formula for the inverse of a product of matrices explicitly represents bn as an integral linear combination of \(a1\) and \(b1.\) Our talk discussed similar recursions arising in continued fractions, filter design, wave propagation in layered media, and quantum physics.