# 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.