Polynomials and lemniscates of indefiniteness

Tutkimustuotos: Lehtiartikkelivertaisarvioitu

Tutkijat

Organisaatiot

Kuvaus

For a large indefinite linear system, there exists the option to directly precondition for the normal equations. Matrix nearness problems are formulated to assess the attractiveness of this alternative. Polynomial preconditioning leads to polynomial approximation problems involving lemniscate-like sets, both in the plane and in C-nxn. A natural matrix analytic extension for lemniscates is introduced. Operator theoretically one is concerned with polynomial unitarity and associated factorizations for the inverse. For the speed of convergence and lemniscate asymptotics, the notion of quasilemniscate arises. In the L-2-norm algorithms for solving the problem are devised.

Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut233-253
Sivumäärä21
JulkaisuNumerische Mathematik
Vuosikerta133
Numero2
TilaJulkaistu - kesäkuuta 2016
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

ID: 1980077