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.