We give a short account on the methods for numerical inversion of the Laplace transform and also propose a new method. Our method is inspired and motivated from a problem of the evaluation of the Müntz polynomials (see [1]), as well as the construction of the generalized Gaussian quadrature rules for the Müntz systems (see [2]). As an illustration of our method we consider an example with 100 r...

.........................................................................................iii LIST OF FIGURES..................................................................................ix ACKNOWLDEGEMENTS........................................................................xv DEDICATION......................................................................................xvii Chapter 1: I...

Aims. We present an analytic approximate seismic inversion scheme for damped transverse coronal loop oscillations based on the thin tube and thin boundary approximation for computing the period and the damping time. Methods. Asymptotic expressions for the period and damping rate are used to illustrate the process of seismological inversion in a simple and easy to follow manner. The inversion pr...

We propose to use digital memcomputing machines (DMMs), implemented with self-organizing logic gates (SOLGs), to solve the problem of numerical inversion. Starting from fixed-point scalar inversion, we describe the generalization to solving linear systems and matrix inversion. This method, when realized in hardware, will output the result in only one computational step. As an example, we perfor...

Recently, an analytic adjoint-based method of optimal nonlocal boundary control has been proposed for inversion of a waveguide acoustic field using the wide-angle parabolic equation [Meyer & Hermand, J. Acoust. Soc. Am. 117, 2937–2948 (2005)]. In this paper a numerical extension of this approach is presented that allows the direct inversion for the geoacoustic parameters which are embedded in a...