Stefan Kindermann, Werner Zellinger,
"A short-term rational Krylov method for linear inverse problems"
, in Electronic Transactions on Numerical Analysis (ETNA), Vol. 60, Seite(n) 327-350, 2024
Original Titel:
A short-term rational Krylov method for linear inverse problems
Sprache des Titels:
Englisch
Original Kurzfassung:
Motivated by the aggregation method, we present an
iterative method for finding approximate solutions of least-squares problems for linear ill-posed problems over (mixed)
rational Krylov spaces. The mixed rational Krylov spaces where the solution is sought consist of Tikhonov-regularized solutions mixed with usual Krylov space elementsfrom the normal equations. We present an algorithm based on the Arnoldi--Lanczos iteration, and, as main result, derive the rational CG method,
a short-term iteration that, similar as the usual conjugate gradient method, does not requires orthogonalization or saving of the Krylov basis vectors. Some numerical experiments illustrate the performance of the method.
Sprache der Kurzfassung:
Englisch
Journal:
Electronic Transactions on Numerical Analysis (ETNA)