In this paper we consider the application of polynomial root-finding methods to the solution of the tridiagonal matrix eigenproblem. All considered solvers are based on evaluating the Newton correction. We show that the use of scaled three-term recurrence relations complemented with error free transformations yields some compensated schemes which significantly improve the accuracy of computed results at a modest increase in computational cost. Numerical experiments illustrate that under some restriction on the conditioning the novel iterations can approximate and/or refine the eigenvalues of a tridiagonal matrix with high relative accuracy.
Accurate polynomial root-finding methods for symmetric tridiagonal matrix eigenproblems
GEMIGNANI, LUCA
2016-01-01
Abstract
In this paper we consider the application of polynomial root-finding methods to the solution of the tridiagonal matrix eigenproblem. All considered solvers are based on evaluating the Newton correction. We show that the use of scaled three-term recurrence relations complemented with error free transformations yields some compensated schemes which significantly improve the accuracy of computed results at a modest increase in computational cost. Numerical experiments illustrate that under some restriction on the conditioning the novel iterations can approximate and/or refine the eigenvalues of a tridiagonal matrix with high relative accuracy.File | Dimensione | Formato | |
---|---|---|---|
newtoncomp_rev1_1.pdf
accesso aperto
Tipologia:
Documento in Post-print
Licenza:
Creative commons
Dimensione
290.36 kB
Formato
Adobe PDF
|
290.36 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.