Results 271 to 280 of about 17,806 (305)

Windowed Spectral Regularization of Inverse Problems

SIAM Journal on Scientific Computing, 2011
Regularization is used in order to obtain a reasonable estimate of the solution to an ill-posed inverse problem. One common form of regularization is to use a filter to reduce the influence of components corresponding to small singular values, perhaps using a Tikhonov least squares formulation.
Julianne Chung, Glenn R. Easley, Dianne P. O'Leary   +2 more
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Designing Optimal Spectral Filters for Inverse Problems

SIAM Journal on Scientific Computing, 2011
Summary: Spectral filtering suppresses the amplification of errors when computing solutions to ill-posed inverse problems; however, selecting good regularization parameters is often expensive. In many applications, data are available from calibration experiments. In this paper, we describe how to use such data to precompute optimal spectral filters. We
Julianne Chung, Matthias Chung, Dianne P. O'Leary   +2 more
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On an inverse spectral problem

Russian Journal of Mathematical Physics, 2017
The author considers the inverse spectral problem of reconstructing a function \(Q\) appearing in \[ (Qy')' +\lambda (y(x)-ky''(x))=0\text{ for }0\leq x \leq 1, \] where \(y\) is subject to \[ y(0)=y(1)=0,\, \int_0^1 y(x)dx=0 \] for \(k>0\). The sought \(Q\) is normalized by \(\int_0^1 Q(x)dx=1\) and the question is to find \(Q\) that minimizes the ...
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On the Uniqueness of the Solution of an Inverse Spectral Problem

Differential Equations, 2003
A uniqueness theorem is proved for the inverse spectral problem of recovering coefficients of the boundary conditions from the spectrum of the boundary value problem \[ y''+p_1(x)y'+(\lambda^2 p_{20}(x)+\lambda p_{21}(x)+p_{22}(x))y=0 ...
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SPECTRAL INVERSE PROBLEM IN SUPERSYMMETRIC QUANTUM MECHANICS

International Journal of Modern Physics A, 1993
The supersymmetric WKB quantization condition is used to study the so-called spectral inverse problem. Wavefunctions for the harmonic oscillator and hydrogen atom are obtained from the knowledge of their bound-state energy spectra. The analysis presented is based essentially on a repackaging of the conventional theory of integral equations.
Bera, P. K., Bhattacharyya, S., Talukdar, B.   +2 more
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Spectral Analysis of an Inverse Problem

2013
In this chapter we treat the solution of systems of linear equations in finite dimension spaces. This can be seen as examples of inverse reconstruction problems of Type I.We present a mathematical analysis of these linear inverse problems of finite dimension based on the spectral theorem.We study several aspects and behaviour of well-established ...
Francisco Duarte Moura Neto, Antônio José da Silva Neto   +1 more
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An inverse spectral problem for the Laplacian

Applicable Analysis, 2005
We propose an algorithm for the recovery of a potential from the knowledge of the eigenvalues of the Laplacian operator and the traces of its eigenfunctions. This inverse spectral problem is solved by recasting the operator as an infinite matrix and using transition matrices together with spectral projections on the boundary.
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The Zakharov–Shabat inverse spectral problem for operators

Journal of Mathematical Physics, 1993
Many soliton equations, their solutions and their properties, can be deduced from simpler (essentially linear) equations involving more complicated objects, e.g., integral operators. The deduction process from the operator-valued equation to the scalar one amounts to some rather simple procedure like taking a trace or a determinant.
Bauhardt, Wolfgang, Pöppe, Christoph
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Spectral and scattering inverse problems

Journal of Mathematical Physics, 1978
The reconstruction of a differential operator form discrete spectra is reduced to its reconstruction from an S-matrix. This method makes it possible to solve the singular Sturm–Liouville problems which determine certain modes of a sphere. The results pave the way for handling studies in which information on modes and scattering results would all be ...
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Spectral techniques in inverse stokes and Overdetermined problems

Surveys in Geophysics, 1993
This paper deals with spectral techniques applied to geodetic problems. The solutions of the Inverse Stokes problem and of the Overdetermined Boundary Value Problem have been obtained applying The Wiener principle directly in the spectral domain.
BARZAGHI, RICCARDO, A. Fermi, S. Tarantola, SANSO', FERNANDO   +3 more
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