Many problems in physics like reconstruction of the radially distributed emissivity from the line-of-sight projected intensity, the 3-D image reconstruction from cone-beam projections in computerized tomography, etc. lead naturally, in the case of radial symmetry, to the study of Abel’s type integral equation. In this paper, a new stable algorithm based on shifted Chebyshev polynomial approxima...

Single-track hard disk drive (HDD) seek performance is measured by settle time, ts, defined as the time from the arrival of a seek command until the measured position reaches and stays within an acceptable distance from the target track. In this paper, we show the effective use of feedforward dynamic inversion, coupled with an aggressive desired trajectory yd, to achieve high performance settle...

It has been shown that approximate extended Krylov subspaces can be computed –under certain assumptions– without any explicit inversion or system solves. Instead the necessary products A−1v are obtained in an implicit way retrieved from an enlarged Krylov subspace. In this paper this approach is generalized to rational Krylov subspaces, which contain besides poles at infinite and zero also fini...

An inverse method based on local approximate solutions (LAS inverse method) is proposed to invert transient flows in heterogeneous aquifers. Unlike the objective-function-based inversion techniques, the method does not require forward simulations to assess measurement-to-model misfits; thus the knowledge of aquifer initial conditions (IC) and boundary conditions (BC) is not required. Instead, t...

Contents Abstract Sinc approximation methods excel for problems whose solutions may have singularities, or innnite domains, or boundary layers. This article summarizes results obtained to date, on Sinc numerical methods of computation. Sinc methods provide procedures for function approximation over bounded or unbounded regions, encompassing interpolation, approximation of derivatives, approxima...

We show how certain widely used multistep approximation algorithms can be interpreted as instances of an approximate Newton method. It was shown in an earlier paper by the second author that the convergence rates of approximate Newton methods (in the context of the numerical solution of PDEs) suuer from a \loss of derivatives", and that the subsequent linear rate of convergence can be improved ...

In this paper an inversion method for the solution of ill-posed linear problems is presented. It is based on the idea of computing a mollified version of the searched-for solution and the approximate inverse operator is computed with exactly given quantities. The method is compared with known methods such as the Tikhonov-Phillips and Backus-Gilbert methods. Numerical tests verify the advantages...