PROFESOR: Gilbert Strang (Massachussets Institute of Technology (MIT))
TITULO: “Inverses and Factorizations of Banded Matrices”.
FECHA Y HORA: Jueves, 13 de octubre a las 9:30h.
LUGAR: Aula 0.3, Escuela Técnica Superior de Ingeniería Informática, edificio 1E.
ABSTRACT: The inverse of a tridiagonal matrix has the special property that if a submatrix does not cross the diagonal, its rank is 1 or 0. As the bandwidth increases, the ranks increase.
If BOTH the matrix A and its inverse are banded, then we can factor into A = BC where B and C are block-diagonal. We also discuss new factorizations of infinite matrices.
I will describe applications (including wavelet matrices) with this unusual property. There are important questions still to answer when the nonzero structure of A comes from a graph (tridiagonal comes from the simplest graph, a line of nodes). Especially important graphs are 2-dimensional grids.