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  • 1
    Electronic Resource
    Electronic Resource
    Compound Poisson approximation for unbounded functions on a group, with application to large deviations (1995)
    Springer
    Probability theory and related fields 103 (1995), S. 515-528 
    Details
    ISSN: 1432-2064
    Keywords: 60B10 ; 60F05 ; 60F10 ; 60B15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A second order error bound is obtained for approximating ∫h d $$\tilde Q$$ by ∫h d $$\tilde Q$$ , where $$\tilde Q$$ is a convolution of measures andQ a compound Poisson measure on a measurable abelian group, and the functionh is not necessarily bounded. This error bound is more refined than the usual total variation bound in the sense that it contains the functionh. The method used is inspired by Stein's method and hinges on bounding Radon-Nikodym derivatives related to $${{d\tilde Q} \mathord{\left/ {\vphantom {{d\tilde Q} {dQ}}} \right. \kern-\nulldelimiterspace} {dQ}}$$ . The approximation theorem is then applied to obtain a large deviation result on groups, which in turn is applied to multivariate Poisson approximation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01246337
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Modified Partial-Update Newton-Type Algorithms for Unary Optimization (1998)
    Springer
    Journal of optimization theory and applications 97 (1998), S. 385-406 
    Details
    ISSN: 1573-2878
    Keywords: Unary optimization ; trust-region methods ; indefinite dogleg curve ; Bunch–Parlett factorization ; rank-one update
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we propose two modified partial-update algorithms for solving unconstrained unary optimization problems based on trust-region stabilization via indefinite dogleg curves. The two algorithms partially update an approximation to the Hessian matrix in each iteration by utilizing a number of times the rank-one updating of the Bunch–Parlett factorization. In contrast with the original algorithms in Ref. 1, the two algorithms not only converge globally, but possess also a locally quadratic or superlinear convergence rate. Furthermore, our numerical experiments show that the new algorithms outperform the trust-region method which uses the partial update criteria suggested in Ref. 1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022682818387
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    Paper (German National Licenses)
    Fulltext
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