Incomplete Data problems in X-Ray Computerized Tomography. II. Truncated Projections and Region-of-Interest Tomography.
Incomplete Data Problems in X-Ray Computerized Tomography. I. Singular Value Decomposition of the Limited Angle Transform.
Integral equations of the third kind
Integral Equations VIA Saddle Point Problem for 2D Electromagnetic Problems
A new system of integral equations for the exterior 2D time harmonic scattering problem is investigated. This system was first proposed by B. Després in [11]. Two new derivations of this system are given: one from elementary manipulations of classical equations, the other based on a minimization of a quadratic functional. Numerical issues are addressed to investigate the potential of the method.
Integral Equations with Transform Kernels and the Eigenproblem KCx = ...x.
Introduction to magnetic resonance imaging for mathematicians
The basic concepts and models used in the study of nuclear magnetic resonance are introduced. A simple imaging experiment is described, as well as, the reduction of the problem of selective excitation to a classical problem in inverse scattering.
Inverse scattering via nonlinear integral equations method for a sound-soft crack with phaseless data
We consider the inverse scattering of time-harmonic plane waves to reconstruct the shape of a sound-soft crack from a knowledge of the given incident field and the phaseless data, and we check the invariance of far field data with respect to translation of the crack. We present a numerical method that is based on a system of nonlinear and ill-posed integral equations, and our scheme is easy and simple to implement. The numerical implementation is described and numerical examples are presented to...
Inversion of the Laplace transform from the real axis using an adaptive iterative method.
Inverted finite elements : a new method for solving elliptic problems in unbounded domains
In this paper, we propose a new numerical method for solving elliptic equations in unbounded regions of . The method is based on the mapping of a part of the domain into a bounded region. An appropriate family of weighted spaces is used for describing the growth or the decay of functions at large distances. After exposing the main ideas of the method, we analyse carefully its convergence. Some 3D computational results are displayed to demonstrate its efficiency and its high performance.
Inverted finite elements: a new method for solving elliptic problems in unbounded domains
In this paper, we propose a new numerical method for solving elliptic equations in unbounded regions of . The method is based on the mapping of a part of the domain into a bounded region. An appropriate family of weighted spaces is used for describing the growth or the decay of functions at large distances. After exposing the main ideas of the method, we analyse carefully its convergence. Some 3D computational results are displayed to demonstrate its efficiency and its high performance.
Iterative Berechnung mehrfacher Lösungen von Hammersteinschen Integralgleichungen.
Iterative sinc-convolution method for solving radiosity equation in computer graphics.
Iterative Variants of the Nyström Method for the Numerical Solution of Integral Equations.
Iteratively solving a kind of Signorini transmission problem in a unbounded domain
In this paper, we are concerned with a kind of Signorini transmission problem in a unbounded domain. A variational inequality is derived when discretizing this problem by coupled FEM-BEM. To solve such variational inequality, an iterative method, which can be viewed as a variant of the D-N alternative method, will be introduced. In the iterative method, the finite element part and the boundary element part can be solved independently. It will be shown that the convergence speed of this iteration...
Iteratively solving a kind of signorini transmission problem in a unbounded domain
In this paper, we are concerned with a kind of Signorini transmission problem in a unbounded domain. A variational inequality is derived when discretizing this problem by coupled FEM-BEM. To solve such variational inequality, an iterative method, which can be viewed as a variant of the D-N alternative method, will be introduced. In the iterative method, the finite element part and the boundary element part can be solved independently. It will be shown that the convergence speed of this iteration...
Konstruktion und algebraische Eigenschaften von M-Spline-Interpolierenden.
and error estimates for mixed methods for integro-differential equations of parabolic type
Laguerre polynomials in the inversion of Mellin transform
In order to use the well known representation of the Mellin transform as a combination of two Laplace transforms, the inverse function is represented as an expansion of Laguerre polynomials with respect to the variable . The Mellin transform of the series can be written as a Laurent series. Consequently, the coefficients of the numerical inversion procedure can be estimated. The discrete least squares approximation gives another determination of the coefficients of the series expansion. The last...
Laplace transforms and the American straddle.
Laplace-Stieltjes transform of the system mean lifetime via geometric process model
Operation principle of the engineering systems occupies an important role in the reliability theory. In most of the studies, the reliability function of the system is obtained analytically according to the structure of the system. Also in such studies the mean operating time of the system is calculated. However, the reliability function of some systems, such as repairable system, cannot be easily obtained analytically. In this case, forming Laplace-Stieltjes transform of the system can provide a...