Daniele Bertaccini

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In this paper, a recently introduced block circulant preconditioner for the linear systems of the codes for ordinary differential equations (ODEs) is investigated. Most ODE codes based on implicit formulas, at each integration step, need the solution of one or more unsymmetric linear systems that are often large and sparse. Here, the boundary value methods,(More)
In this paper we consider the problem of preconditioning symmetric positive definite matrices of the form Aα = A+αI where α > 0. We discuss how to cheaply modify an existing sparse approximate inverse preconditioner for A in order to obtain a preconditioner for Aα. Numerical experiments illustrating the performance of the proposed approaches are presented.(More)
Time-domain numerical solutions of a nonlinear active cochlear model forced by click stimuli are analyzed with a time-frequency wavelet technique to identify the components of the otoacoustic response associated with different generation mechanisms/places. Previous experimental studies have shown evidence for the presence of at least two components in the(More)
We revisit real-valued preconditioned iterative methods for the solution of complex linear systems, with an emphasis on symmetric (non-Hermitian) problems. Different choices of the real equivalent formulation are discussed, as well as different types of block preconditioners for Krylov subspace methods. We argue that if either the real or the symmetric part(More)
A nonlinear and non-local cochlear model has been efficiently solved in the time domain numerically, obtaining the evolution of the transverse displacement of the basilar membrane at each cochlear place. This information allows one to follow the forward and backward propagation of the traveling wave along the basilar membrane, and to evaluate the(More)
The solution of ordinary and partial differential equations using implicit linear multistep formulas (LMF) is considered. More precisely, boundary value methods (BVMs), a class of methods based on implicit formulas will be taken into account in this paper. These methods require the solution of large and sparse linear systems M̂x = b. Block-circulant(More)
The numerical solution of large and sparse nonsymmetric linear systems of algebraic equations is usually the most time consuming part of time-step integrators for differential equations based on implicit formulas. Preconditioned Krylov subspace methods using Strang block circulant preconditioners have been employed to solve such linear systems. However, it(More)
A fast full second order time-step algorithm for some recently proposed nonlinear, nonlocal active models for the inner ear is analyzed here. In particular, we emphasize the properties of discretized systems and the convergence of a hybrid direct-iterative solver for its approximate solution in view of the parameters of the continuous model. We found that(More)