Numerical Analysis and Scientific Computing Seminar

Approximating low-rank eigenpairs of matrix-valued linear operators

Speaker: Nicola Guglielmi, Gran Sasso Science Institute, Italy

Location: Warren Weaver Hall 1302

Date: Feb. 21, 2020, 10 a.m.

Synopsis:

In several applications, in particular PDEs, one is interested to compute eigensolutions
of a matrix valued linear operator. In this talk I will present a new method to approximate the rightmost
eigenpair of a matrix-valued linear operator, in a low-rank setting.
 First I will introduce a suitable ordinary differential equation, whose solution allows us to approximate
the rightmost eigenpair of the linear operator and will analyze the behavior of its solution on the whole
space. Then the ODE is projected on a low-rank manifold of prescribed rank and I will present some methods
to compute it efficiently. Some experiments will illustrate the behavior of the method.

 This is based on a joint research with D. Kressner and C. Scalone.