COSAM » Events » 2016 » February » Applied Mathematics Seminar

 Applied Mathematics Seminar Time: Feb 12, 2016 (01:00 PM) Location: Parker Hall 352 Details: 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.

Last updated: 02/09/2016