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

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### 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

... 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

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### 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

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### 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

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### 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

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### 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

... 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

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### 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

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### 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

... 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

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### 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

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### 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

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### 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

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### 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

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### 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

... 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

... 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

... 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

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### 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

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### 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

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