2025-07-24 –, Lawrence Room 120 - REPL Main Stage
Solving a linear system is one of the oldest problems in mathematics. Prof John Urschel, at MIT Mathematics, will present the history of the elimination algorithm, one of the most fundamental techniques to solve linear systems.
The solution of a linear system, i.e., given a matrix A and vector b, finding a vector x satisfying Ax = b, is one of the oldest problems in mathematics. Gaussian elimination is one of the most fundamental and well-known techniques for solving linear systems, by factoring a matrix into the product of a lower and upper triangular matrix. Surprisingly, a number of questions regarding the numerical stability of this algorithm remains. In this talk, we will study the history of this subject, a story that spans eighty years, and discuss some recent progress. We'll also highlight the role of Julia in this progress.
