In the last decades, helicopter-borne electromagnetic (HEM) method became a focus of interest in the fields of mineral exploration, geological mapping, groundwater resource investigation and environmental monitoring. As a standard approach, researchers use 1-D inversion of the acquired HEM data to recover the conductivity/resistivity-depth models. Since the relation between HEM data and model ...

Non-linear image reconstruction methods are desirable for applications in electrical impedance tomography (EIT) such as brain or breast imaging where the assumptions of linearity are violated. We present a novel non-linear Newton-Krylov method for solving large-scale EIT inverse problems, which has the potential advantages of improved robustness and computational efficiency over previous method...

Szegö quadrature formulas represent the analogue on the unit circle of the well-known Gauss–Christoffel quadratures for intervals of the real line. In the present work, Szegö formulas are revised and an application to the computation of the Fourier transform given. 2006 Elsevier Inc. All rights reserved.

Goldschmidt’s Algorithms for division and square root are often characterized as being useful for hardware implementation, and lacking self-correction. A reexamination of these algorithms show that there are good software counterparts that retain the speed advantage of Goldschmidt’s Algorithm over the Newton-Raphson iteration. A final step is needed, however, to get the last bit rounded correctly.

A likelihood approach for 0tting asymmetric stochastic volatility models is proposed. It is 0rst shown that, using a quadrature method, the likelihood of these models may be approximated, with the required level of accuracy, by a function that may be easily evaluated using matrix calculus along with its 0rst and second derivatives. The approximated likelihood may be maximized using a standard N...

In this paper we consider level-set-based methods for anomaly reconstruction for applications involving low-sensitivity data concentrating specifically on the problem of electrical resistance tomography (ERT). Typical descent-based inversion methods suffer from poor reconstruction precision in low-sensitivity regions and typically display quite slow convergence. In this paper, we develop a meth...

We describe a strategy for rigorous arbitrary-precision evaluation of Legendre polynomials on the unit interval and its application in the generation of Gauss-Legendre quadrature rules. Our focus is on making the evaluation practical for a wide range of realistic parameters, corresponding to the requirements of numerical integration to an accuracy of about 100 to 100 000 bits. Our algorithm com...

Consider a complex sequence {λk}k=0 convergent to λ∗ ∈ C with order p ∈ N. The convergence factor is typically defined as the fraction ck := (λk+1 − λ∗)/(λk − λ∗) in the limit k → ∞. In this paper we prove formulas characterizing ck in the limit k → ∞ for two different Newton-type methods for nonlinear eigenvalue problems. The formulas are expressed in terms of the left and right eigenvectors. ...