[Crib-list] AMC Monday Sept 9: Exploiting Tropical Algebra in Numerical Linear Algebra

[Yufei An]

Dear All,

The first Applied Math Colloquium of the academic year has been scheduled.  We hope you can join us.

Date: Monday, September 09, 2024
Time: 4:30 PM - 5:30 PM
Location: Room 2 – 190

Speaker:  Françoise Tisseur<https://personal.maths.manchester.ac.uk/tisseur/> (The University of Manchester<https://www.manchester.ac.uk/>)
Title: Exploiting Tropical Algebra in Numerical Linear Algebra
Abstract: The tropical semiring consists of the real numbers and infinity along with two binary operations: addition defined by the max or min operation and multiplication. Tropical algebra is the tropical analogue of linear algebra, working with matrices with entries on the extended real line. There are analogues of eigenvalues and singular values of matrices, and matrix factorizations in the tropical setting, and when combined with a valuation map these analogues  offer `order of magnitude' approximations to eigenvalues and singular values, and factorizations of matrices in the usual algebra. What makes tropical algebra a useful tool for numerical linear algebra is that these tropical analogues are usually cheaper to compute than those in the conventional algebra. They can then be used in the design of preprocessing steps to improve the numerical behaviour of algorithms. In this talk I will review the contributions of tropical algebra to numerical linear algebra and discuss recent results on the selection of Hungarian scalings prior to solving linear systems and eigenvalue problems.

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