Abstract
AbstractWe are interested in generalized matrix eigenvalue problems of the type $$A X + X A = \lambda {H} X {H}$$
A
X
+
X
A
=
λ
H
X
H
and $$A X + X A = \lambda ({H} X + X {H})$$
A
X
+
X
A
=
λ
(
H
X
+
X
H
)
with A and H both symmetric and positive definite, and in their tensor counterparts. We collect several structural properties, some of which are known, together with some new spectral results. We also analyze in detail the case where the second problem stems from the discretization of linear elliptic partial differential equations by finite differences. In particular, we derive spectral properties that can be used in the numerical solution of the resulting algebraic linear system.
Funder
Gruppo Nazionale per il Calcolo Scientifico
Publisher
Springer Science and Business Media LLC
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