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[PDF] Top 20 Numerical methods for ill-posed, linear problems

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Numerical methods for ill-posed, linear problems

Numerical methods for ill-posed, linear problems

... R., ''Some Numerical Results for the Solution of the Heat Equation Backwards in Time," Numerical Solutions of Nonlinear Differential Equations. , Stability of Bou[r] ... See full document

130

Numerical methods for experimental design of large-scale linear ill-posed inverse problems

Numerical methods for experimental design of large-scale linear ill-posed inverse problems

... inverse linear problems has been well studied, covering a vast range of well-established design criteria and optimization algorithms, its ill-posed counterpart is a rather new ...The ... See full document

21

CiteSeerX — Polytope samplers for inference in ill-posed inverse problems

CiteSeerX — Polytope samplers for inference in ill-posed inverse problems

... ever, partitioning a polytope into mutually exclusive simplexes is a non-trivial operation. An efficient algo- rithm to produce such decompositions is needed. The moment-map sampler is a direct method that general- izes ... See full document

9

Discrete ill-posed least-squares problems with a solution norm constraint

Discrete ill-posed least-squares problems with a solution norm constraint

... discrete ill-posed least-squares problems with error-contaminated data does not, in general, give meaning- ful results, because propagated error destroys the computed so- ...discuss numerical ... See full document

18

GMRES implementations and residual smoothing techniques for solving ill-posed linear systems

GMRES implementations and residual smoothing techniques for solving ill-posed linear systems

... iterative methods like GMRES, LSQR and ...solving linear system of ...solving ill-posed linear problems are applied to know which GMRES algorithm, with what extent, is more ... See full document

13

Analytical and Iterative Regularization Methods for Nonlinear Ill-posed Inverse Problems: Applications to Diffuse Optical and Electrical Impedance Tomography

Analytical and Iterative Regularization Methods for Nonlinear Ill-posed Inverse Problems: Applications to Diffuse Optical and Electrical Impedance Tomography

... Clearly, the reconstructions are strongly dependent on the choice of the regularization parameters. There is a vast literature for choosing optimal regularization parameters for linear problems. However, ... See full document

139

Ill-Posed and Linear Inverse Problems

Ill-Posed and Linear Inverse Problems

... paper ill-posed linear inverse problems that arises in many applications is ...these problems and it’s relation to the kernel, is ...these problems we need some kind of ... See full document

8

Cascadic multilevel methods for ill-posed problems

Cascadic multilevel methods for ill-posed problems

... Multilevel methods are popular for the solution of well-posed problems, such as certain boundary value problems for partial differential equations and Fredholm integral equations of the second ... See full document

12

Iterative regularization methods for ill-posed problems

Iterative regularization methods for ill-posed problems

... and ill-posed problems, a great deal of attention has been devoted to the regularization in the Banach space ...regularization methods in Banach spaces was driven by different mathematical ... See full document

272

A new method for solving linear ill-posed problems

A new method for solving linear ill-posed problems

... i σ 2 i +λ 2 ∈ [0, 1] are the Tikhonov filter factors. As mentioned in the intro- duction, a variety of parameter choice methods can be used to determine λ. Here we just describe GCV, for the introduction of W-GCV ... See full document

19

Ill-Posed Problems

Ill-Posed Problems

... exist problems in which solution error are the same order of magnitude as error in setting coefficients; this case is simplest to ...are problems wherein solution errors are greater than coefficient ...are ... See full document

9

Lagrangian methods for the regularization of discrete ill-posed problems

Lagrangian methods for the regularization of discrete ill-posed problems

... Other methods do not require the exact knowl- edge of σ but try to derive such information from the right-hand side ...heuristic methods. Very popular methods of such type are the L-curve criterion ... See full document

60

Fractional regularization matrices for linear discrete ill-posed problems

Fractional regularization matrices for linear discrete ill-posed problems

... severely ill-conditioned and may be singular. This kind of least-squares problems often are referred to as discrete ill-posed ...of linear ill-posed problems, such ... See full document

21

Solution of Linear Ill-posed Problems Using Overcomplete Dictionaries

Solution of Linear Ill-posed Problems Using Overcomplete Dictionaries

... ing a probability distribution. The random matrices have wide applications in various branches of science and technology, out of which in this dissertation, we have only considered its application in Compressed sensing. ... See full document

87

Estimation and Clustering in Statistical Ill-posed Linear Inverse Problems

Estimation and Clustering in Statistical Ill-posed Linear Inverse Problems

... Chapter 4 is devoted to the issue of clustering in statistical ill-posed linear inverse problems investigated in [58]. Section 4.1 describe the Notation. Section 4.2 introduces problem and its ... See full document

130

Expanding the applicability of Lavrentiev regularization methods for ill-posed problems

Expanding the applicability of Lavrentiev regularization methods for ill-posed problems

... an ill-posed problem in a Hilbert space setting using the Lavrentiev regularization method and, in particular, expanding the applicability of this method by weakening the popular Lipschitz-type hypotheses ... See full document

15

Numerical study of two ill-posed one phase Stefan problems

Numerical study of two ill-posed one phase Stefan problems

... boundary problems. The first is the ill- posed Stefan problem for melting a superheated solid in one Cartesian ...existing numerical results, concentrating on solutions that break down in ... See full document

17

Ill-posed inverse problems in economics

Ill-posed inverse problems in economics

... 1 ILL-POSED INVERSE PROBLEMS IN ECONOMICS ...a linear model, the parameter of interest is a scalar or vector, and the identifying mapping is ... See full document

60

Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems

Posterior contraction rates for the Bayesian approach to linear ill-posed inverse problems

... In Section 5 , we present a new method of identify- ing the posterior distribution: we first characterize it through its Radon-Nikodym derivative with respect to the prior (Theorem 5.1 )[r] ... See full document

43

An extrapolated TSVD method for linear discrete ill-posed problems with Kronecker structure

An extrapolated TSVD method for linear discrete ill-posed problems with Kronecker structure

... new numerical method for the solution of large linear discrete ill-posed problems, whose matrix is a Kro- necker ...product. Problems of this kind arise, for instance, from the ... See full document

12

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