Abstract:

In 1951, Alston Householder of Oak Ridge National Laboratory formalizes the decompositional approach to matrix computations. The approach is selected as one of the top 10 algorithms with the greatest influence on science, numerical analysis, and engineering in the 20th century in the January/February 2000 issue of Computing in Science and Engineering. In this talk, we will discuss the motivations, ideas, and history of some matrix decompositions including LU decomposition and singular value decompositoin. Moreover, we will present a novel numerical algorithm for solving Poisson equation designed by taking advantage of a matrix decomposition associated with the Legendre polynomials. Finally, we use some numerical examples to show the necessity of designing a viable numerical algorithm with the aid of useful matrix decompositions.