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- Elfving, Tommy, 1944-, et al.
(författare)
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Semi-convergence and relaxation parameters for a class of SIRT algorithms
- 2010
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Ingår i: Electronic Transactions on Numerical Analysis. - : Kent State University Library. - 1068-9613. ; 37, s. 321-336
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Tidskriftsartikel (refereegranskat)abstract
- This paper is concerned with the Simultaneous Iterative Reconstruction Technique (SIRT) class of iterative methods for solving inverse problems. Based on a careful analysis of the semi-convergence behavior of these methods, we propose two new techniques to specify the relaxation parameters adaptively during the iterations, so as to control the propagated noise component of the error. The advantage of using this strategy for the choice of relaxation parameters on noisy and ill-conditioned problems is demonstrated with an example from tomography
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| 3. |
- Jarlebring, Elias, et al.
(författare)
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A spatially adaptive iterative method for a class of nonlinear operator eigenvalue problems
- 2014
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Ingår i: Electronic Transactions on Numerical Analysis. - : Kent State University Press. - 1068-9613. ; 41, s. 21-42-
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Tidskriftsartikel (refereegranskat)abstract
- We present a new algorithm for the iterative solution of nonlinear operator eigenvalue problems arising from partial differential equations (PDEs). This algorithm combines automatic spatial resolution of linear operators with the infinite Arnoldi method for nonlinear matrix eigenproblems proposed by Jarlebring et al. [Numer.Math., 122 (2012), pp. 169–195]. The iterates in this infinite Arnoldi method are functions, and each iteration requires the solution of an inhomogeneous differential equation. This formulation is independent of the spatial representation of the functions, which allows us to employ a dynamic representation with an accuracy of about the level of machine precision at each iteration similar to what is done in the Chebfun system with its chebop functionality although our function representation is entirely based on coefficients instead of function values. Our approach also allows nonlinearity in the boundary conditions of the PDE. The algorithm is illustrated with several examples, e.g., the study of eigenvalues of a vibrating string with delayed boundary feedback control.
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| 4. |
- Nilsson Jacobi, Martin, 1972
(författare)
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A Robust Spectral Method for Finding Lumpings and Meta Stable States of Non-Reversible Markov Chains
- 2010
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Ingår i: Electronic Transactions on Numerical Analysis. - 1068-9613 .- 1097-4067. ; 37, s. 296-306
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Tidskriftsartikel (refereegranskat)abstract
- A spectral method for identifying lumping in large Markov chains is presented. The identification of meta stable states is treated as a special case. The method is based on the spectral analysis of a self-adjoint matrix that is a function of the original transition matrix. It is demonstrated that the technique is more robust than existing methods when applied to noisy non-reversible Markov chains.
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