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- Gulliksson, Mårten, et al.
(författare)
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Perturbation identities for regularized Tikhonov inverses and weighted pseudoinverses
- 2000
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Ingår i: Bit: numerical mathematics. - 0006-3835. ; 40:3, s. 513-523
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Tidskriftsartikel (refereegranskat)abstract
- e consider the perturbation analysis of two important problems for solving ill-conditioned or rank-deficient linear least squares problems. The Tikhonov regularized problem is a linear least squares problem with a regularization term balancing the size of the residual against the size of the weighted solution. The weight matrix can be a non-square matrix (usually with fewer rows than columns). The minimum-norm problem is the minimization of the size of the weighted solutions given by the set of solutions to the, possibly rank-deficient, linear least squares problem. It is well known that the solution of the Tikhonov problem tends to the minimum-norm solution as the regularization parameter of the Tikhonov problem tends to zero. Using this fact and the generalized singular value decomposition enable us to make a perturbation analysis of the minimum-norm problem with perturbation results for the Tikhonov problem. From the analysis we attain perturbation identities for Tikhonov inverses and weighted pseudoinverses.
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| 3. |
- Gulliksson, Mårten, et al.
(författare)
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The use and properties of Tikhonov filter matrices.
- 2000
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Ingår i: SIAM Journal on Matrix Analysis and Applications. - 0895-4798. ; 22:1, s. 276-281
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Tidskriftsartikel (refereegranskat)abstract
- We consider the concept of Tikhonov filter matrices in connection with discrete ill-posed and rank-deficient linear problems. Important properties of the Tikhonov filter matrices are given together with their filtering and regularization effects. We also present new perturbation identities for the Tikhonov regularized linear least squares problem using filter matrices generalizing well-known perturbation identities for the linear least squares problem and pseudoinverses.
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| 4. |
- Nyström, L., et al.
(författare)
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A note on some identification problems arising in Roentgen stereo photogrammetric analysis
- 1994
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Ingår i: Journal of Biomechanics. - : Elsevier BV. - 0021-9290 .- 1873-2380. ; 27, s. 1291-1294
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Tidskriftsartikel (refereegranskat)abstract
- When studying skeleton movements by using implanted landmarks and Roentgen Stereo Photogrammetric Analysis (RSA), some identification problems arise. One is to put the same label on a landmark at different examinations, another is to use the correct pairs of landmark images in order to compute a correct 3-D position of each landmark. We will present some methods that can be used as a support for solving these problems. We will also show how it is possible to detect and exclude landmarks that are loose and landmarks that have large measurement errors in their positions.
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