| 1. |
- Ekblom, Håkan
(författare)
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A new algorithm for the huber estimator in linear models
- 1988
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Ingår i: BIT Numerical Mathematics. - 0006-3835 .- 1572-9125. ; 28:1, s. 123-132
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Tidskriftsartikel (refereegranskat)abstract
- This paper considers algorithms for solving the linear robust regression problem by minimizing the Huber function. In the computational methods for this problem used so far, the scale estimate is adjusted separately. The new algorithm, based on Newton's method, treats both the scale and the location parameters as independent variables. The special form of the Hessian allows for an efficient updating scheme.
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| 2. |
- Ekblom, Håkan, et al.
(författare)
-
Algorithms for non linear huber estimation
- 1989
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Ingår i: BIT Numerical Mathematics. - 0006-3835 .- 1572-9125. ; 29:1, s. 60-76
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Tidskriftsartikel (refereegranskat)abstract
- The Huber criterion for data fitting is a combination of thel 1 and thel 2 criteria which is robust in the sense that the influence of wild data points can be reduced. We present a trust region and a Marquardt algorithm for Huber estimation in the case where the functions used in the fit are non-linear. It is demonstrated that the algorithms converge under the usual conditions.
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| 3. |
- Herlestam, Tore, et al.
(författare)
-
On computing logarithms over GF(2p)
- 1981
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Ingår i: BIT Numerical Mathematics. - 0006-3835. ; 21:3, s. 326-334
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we present a new, heuristic method for computing logarithms over GF(2P). When 2P-1 is a Mersenne prime <231-1 it works in very short running times on a general purpose computer. It is based on the interdependent relations f,~(t) = t-2~f(t) 2" and log f~s(t) = - 2' + 2" log f(t), where f and frs are polynomials over GF(2). Its cryptographic significance is discussed and it can be considered as an attempt to swindle MITRE Corporation which reportedly is using a public key distribution system, based on the presumed difficulty in computing logarithms over GF(2127).
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| 4. |
- 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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| 5. |
- Smeets, Ben
(författare)
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On the number of polynomials over GF(2) that factor into 2, 3 or 4 prime polynomials
- 1985
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Ingår i: BIT Numerical Mathematics. - 0006-3835. ; 25, s. 667-674
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Tidskriftsartikel (refereegranskat)abstract
- In this paper a simple method is presented to derive formulas for the number of polynomials over GF(2) which factor into two, three, and four prime polynomials only. A table is given, summarizing the above numbers for polynomials of degree up to 127. Furthermore, the computed values are compared with an asymptotic approximation for these values.
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| 6. |
- Strömberg, Dan, et al.
(författare)
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Transfer of programs from development to runtime environments
- 1980
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Ingår i: BIT Numerical Mathematics. - : Kluwer Academic Publishers. - 0006-3835 .- 1572-9125. ; 20:4, s. 434-442
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Tidskriftsartikel (refereegranskat)abstract
- The transfer of programs from development systems to efficient run-time environments is generally considered as a compilation process possibly followed by an optimization phase. This order excludes most possibilities to make optimizations on the source language level. This paper describes an alternative transfer method where user interaction is done on a user oriented level in order to support the optimization process. Experiments show that the efficiency gain is considerable.
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