In this paper a theoretical error analysis of the recursive superfast algorithm for the solution of Toeplitz-like systems, introduced in [4], is performed. This analysis produces an upper bound to the norm of the residual vector, allowing the detection of some parameters which rule the stability behavior of the algorithm. These parameters take into account both the conditioning properties of the coe±cient matrices at the di®erent levels of recursion and the magnitude of some involved matrices measured through their generators. The experimentation con¯rms the theoretical results, pointing out that, in general, the upper bound to the norm of the residual vector is too pessimistic.
Stability analysis of a superfast algorithm for Toeplitz-like systems
Favati P;
2012
Abstract
In this paper a theoretical error analysis of the recursive superfast algorithm for the solution of Toeplitz-like systems, introduced in [4], is performed. This analysis produces an upper bound to the norm of the residual vector, allowing the detection of some parameters which rule the stability behavior of the algorithm. These parameters take into account both the conditioning properties of the coe±cient matrices at the di®erent levels of recursion and the magnitude of some involved matrices measured through their generators. The experimentation con¯rms the theoretical results, pointing out that, in general, the upper bound to the norm of the residual vector is too pessimistic.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
