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Inverse Problems Light: Numerical Differentiation
The American Mathematical Monthly, 2001(2001). Inverse Problems Light: Numerical Differentiation. The American Mathematical Monthly: Vol. 108, No. 6, pp. 512-521.
Martin Hanke, Otmar Scherzer
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Numerical Stability in an Inverse Scattering Problem
SIAM Journal on Numerical Analysis, 1980The main result of this paper is a stability theorem for a certain class of difference algorithms designed to give approximate solutions of a model inverse scattering problem in one dimension. This stability result guarantees the convergence of the approximate solutions to the exact solution of the problem as the grid of the difference scheme is ...
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An Inverse Problem for the $k$-Rank Numerical Range
SIAM Journal on Matrix Analysis and Applications, 2016Summary: For an \(n \times n\) matrix \(A\) and an integer \(k \in [1,n]\), the concept of the higher rank numerical range \(\Lambda_k(A)=\left\{z \in \mathbb{C}:V^*AV=zI_k, \; V \in \mathbb{C}^{n \times k}, \; V^*V=I_k\right\}\) has been introduced in relation to the study of error correcting codes and has been extensively studied.
Georgios Katsouleas, John Maroulas
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Numerical Solution of a Subsurface Imaging Inverse Problem
SIAM Journal on Applied Mathematics, 2001Summary: A new solution method for an inverse problem for the two-dimensional Helmholtz equation is developed. The underlying application area which motivated this work is the imaging of land mines using ground penetrating radar, formulated as an inverse problem for the Helmholtz equation.
Yuriy A. Gryazin +2 more
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Probabilistic Scaling for the Numerical Inversion of Nonprobability Transforms
INFORMS Journal on Computing, 1997It is known that probability density functions and probability mass functions usually can be calculated quite easily by numerically inverting their transforms (Laplace transforms and generating functions, respectively) with the Fourier-series method. Other more general functions can be substantially more difficult to invert, because the aliasing and ...
Gagan L. Choudhury, Ward Whitt
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A Numerical Method for the Inverse Stochastic Spectrum Problem
SIAM Journal on Matrix Analysis and Applications, 1998This paper concerns the construction of a stochastic matrix with a prescribed spectrum. The present ``flow approach'' is based on a differential equation to obtain the steepest descent flow for reducing the distance (given, say, in terms of the Frobenius norm) between isospectral matrices and nonnegative matrices.
Moody T. Chu, Quanlin Guo
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Numerical methods for elliptic inverse problems
International Journal of Computer Mathematics, 1998Identifying physical parameters in elliptic boundary value problems is formulated as a constrained minimization problem using the output least squares method with the H l-regularization or the BV-regularization. The constrained minimization problem is then discretized by finite element methods and the discretization is shown to be convergent for both ...
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A Numerical Approach to the Inverse Toeplitz Eigenproblem
SIAM Journal on Scientific and Statistical Computing, 1988The author proposes an iterative procedure for the inverse Toeplitz eigenproblems: diagonalize the current approximation \(T_ k\) to the required matrix to determine the corresponding matrix of eigenvectors \(Q_ k\), then construct \(T_{k+1}\) as the Toeplitz matrix which has the given eigenvalues as its Rayleigh quotients associated with the ...
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A Note on the Numerical Inversion of the Laplace Transform
2006The aim of this paper is to show that the recently developed high performance divide and conquer algorithm for finding trigonometric sums can be applied to improve the performance of the Talbot's method for the numerical inversion of the Laplace Transform on modern computer architectures including shared memory parallel computers.
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Numerical inverse computation of reflectivity
High Power Laser and Particle Beams, 2013By analyzing the one-dimensional heat transfer equation under the heat flux boundary condition, a numerical method for inverse computation from the back surface temperature data to the front surface reflectivity data is proposed. The inversely computing program is verified by the positive and inverse computation of one-dimensional heat transfer.
金云声 Jin Yunsheng +6 more
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