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| 3. |
- Ljung, Stefan, et al.
(författare)
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Error Propagation Properties of Recursive Least-Squares Adaptation Algorithms
- 1984
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Ingår i: Proceedings of the 9th IFAC World Congress. - : Pergamon. - 0080316662 ; , s. 70-74
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Konferensbidrag (refereegranskat)abstract
- The numerical properties of implementations of the recursive least-squares identification algorithm are of great importance for their continuous use in various adaptive schemes. Here we investigate how an error that is introduced at an arbitrary point in the algorithm propagates. It is shown that conventional LS algorithms, including Bierman's UD-factorization algorithm are exponentially stable with respect to such errors, i.e. the effect of the error decays exponentially. The base of the decay is equal to the forgetting factor. The same is true for fast lattice algorithms. The fast least-squares algorithm, sometimes known as the ‘fast Kalman algorithm’ is however shown to be unstable with respect to such errors.
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| 4. |
- Ljung, Stefan, et al.
(författare)
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Error Propagation Properties of Recursive Least Squares Adaptation Algorithms
- 1983
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The numerical properties of implementations of the recursive least-squares identification algorithm are of great importance for their continuous use in various adaptive schemes. Here we investigate how an error that is introduced at an arbitrary point in the algorithm propagates. It is shown that conventional LS algorithms, including Bierman's UD-factorization algorithm are exponentially stable with respect to such errors, i.e. the effect of the error decays exponentially. The base of the decay is equal to the forgetting factor. The same is true for fast lattice algorithms. The fast least-squares algorithm, sometimes known as the ‘fast Kalman algorithm’ is however shown to be unstable with respect to such errors.
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| 5. |
- Ljung, Stefan, et al.
(författare)
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Error Propagation Properties of Recursive Least Squares Adaptation Algorithms
- 1985
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 21:2, s. 157-167
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Tidskriftsartikel (refereegranskat)abstract
- The numerical properties of implementations of the recursive least-squares identification algorithm are of great importance for their continuous use in various adaptive schemes. Here we investigate how an error that is introduced at an arbitrary point in the algorithm propagates. It is shown that conventional LS algorithms, including Bierman's UD-factorization algorithm are exponentially stable with respect to such errors, i.e. the effect of the error decays exponentially. The base of the decay is equal to the forgetting factor. The same is true for fast lattice algorithms. The fast least-squares algorithm, sometimes known as the ‘fast Kalman algorithm’ is however shown to be unstable with respect to such errors.
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| 6. |
- Ljung, Stefan, et al.
(författare)
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Fast Numerical Solution of Fredholm Integral Equations with Stationary Kernels
- 1980
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A fast recursive matrix method for the numerical solution of Fredholm integral equations with stationary kernels is derived. IfN denotes the number of nodal points, the complexity of the algorithm isO(N 2), which should be compared toO(N 3) for conventional algorithms for solving such problems. The method is related to fast algorithms for inverting Toeplitz matrices.Applications to equations of the first and second kind as well as miscellaneous problems are discussed and illustrated with numerical examples. These show that the theoretical improvement in efficiency is indeed obtained, and that no problems with numerical stability or accuracy are encountered.
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| 7. |
- Ljung, Stefan, et al.
(författare)
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Fast Numerical Solution of Fredholm Integral Equations with Stationary Kernels
- 1982
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Ingår i: BIT Numerical Mathematics. - : Kluwer Academic Publishers. - 0006-3835 .- 1572-9125. ; 22:1, s. 54-72
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Tidskriftsartikel (refereegranskat)abstract
- A fast recursive matrix method for the numerical solution of Fredholm integral equations with stationary kernels is derived. IfN denotes the number of nodal points, the complexity of the algorithm isO(N 2), which should be compared toO(N 3) for conventional algorithms for solving such problems. The method is related to fast algorithms for inverting Toeplitz matrices.Applications to equations of the first and second kind as well as miscellaneous problems are discussed and illustrated with numerical examples. These show that the theoretical improvement in efficiency is indeed obtained, and that no problems with numerical stability or accuracy are encountered.
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