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  • 1
    Electronic Resource
    Electronic Resource
    Robust window operators (1989)
    Springer
    Machine vision and applications 2 (1989), S. 179-191 
    Details
    ISSN: 1432-1769
    Keywords: robust statistics ; M-estimation ; smoothing ; derivative estimation ; surface fitting ; image filtering
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract It is a common practice in computer vision and image processing to convolve rectangular constant coefficient windows with digital images to perform local smoothing and derivative estimation for edge detection and other purposes. If all data points in each image window belong to the same statistical population, this practice is reasonable and fast. But, as is well known, constant coefficient window operators produce incorrect results if more than one statistical population is present within a window, for example, if a gray-level or gradient discontinuity is present. This paper shows one way to apply the theory of robust statistics to the data smoothing and derivative estimation problem. A robust window operator is demonstrated that preserves gray-level and gradient discontinuities in digital images as it smooths and estimates derivatives.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01215874
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Granularity issues for solving polynomial systems via globally convergent algorithms on a hypercube (1989)
    Springer
    The journal of supercomputing 3 (1989), S. 5-20 
    Details
    ISSN: 1573-0484
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Polynomial systems of equations frequently arise in many applications such as solid modelling, robotics, computer vision, chemistry, chemical engineering, and mechanical engineering. Locally convergent iterative methods such as quasi-Newton methods may diverge or fail to find all meaningful solutions of a polynomial system. Recently a homotopy algorithm has been proposed for polynomial systems that is guaranteed globally convergent (always converges from an arbitrary starting point) with probability one, finds all solutions to the polynomial system, and has a large amount of inherent parallelism. There are several ways the homotopy algorithms can be decomposed to run on a hypercube. The granularity of a decomposition has a profound effect on the performance of the algorithm. The results of decompositions with two different granularities are presented. The experiments were conducted on an iPSC-16 hypercube using actual industrial problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00129645
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Book reviews (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 801-809 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459661
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Convergence analysis for cellular automata applied to truss design (2002)
    Bradford : Emerald
    Engineering computations 19 (2002), S. 953-969 
    Details
    ISSN: 0264-4401
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Technology
    Notes: Traditional parallel methods for structural design, as well as modern preconditioned iterative linear solvers, do not scale well. This paper discusses the application of massively scalable cellular automata (CA) techniques to structural design, specifically trusses. There are two sets of CA rules, one used to propagate stresses and strains, and one to perform design updates. These rules can be applied serially, periodically, or concurrently, and Jacobi or Gauss-Seidel style updating can be done. These options are compared with respect to convergence, speed, and stability for an example, problem of combined sizing and topology design of truss domain structures. The central theme of the paper is that the cellular automaton paradigm is tantamount to classical block Jacobi or block Gauss-Seidel iteration, and consequently the performance of a cellular automaton can be rigorously analyzed and predicted.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1108/02644400210450369
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  • 5
    Electronic Resource
    Electronic Resource
    A fully-distributed parallel global search algorithm (2001)
    Bradford : Emerald
    Engineering computations 18 (2001), S. 155-169 
    Details
    ISSN: 0264-4401
    Source: Emerald Fulltext Archive Database 1994-2005
    Topics: Technology
    Notes: The n-dimensional direct search algorithm, DIRECT, developed by Jones, Perttunen, and Stuckman has attracted recent attention from the multidisciplinary design optimization community. Since DIRECT only requires function values (or ranking) and balances global exploration with local refinement better than n-dimensional bisection, it is well suited to the noisy function values typical of realistic simulations. While not efficient for high accuracy optimization, DIRECT is appropriate for the sort of global design space exploration done in large scale engineering design. Direct and pattern search schemes have the potential to exploit massive parallelism, but efficient use of massively parallel machines is non-trivial to achieve. A fully-distributed control version of DIRECT that is designed for massively parallel (distributed memory) architectures is presented. Parallel results are presented for a multidisciplinary design optimization problem - configuration design of a high speed civil transport.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1108/02644400110365851
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  • 6
    Electronic Resource
    Electronic Resource
    Computational experience with the Chow—Yorke algorithm (1980)
    Springer
    Mathematical programming 19 (1980), S. 92-101 
    Details
    ISSN: 1436-4646
    Keywords: Chow—Yorke Algorithm ; Homotopy Algorithm ; Globally Convergent ; Fixed Point Computation ; Nonlinear Complementarity Problem ; Computational Results ; Convex Minimization Problems ; Nonlinear Equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The Chow—Yorke algorithm is a nonsimplicial homotopy type method for computing Brouwer fixed points that is globally convergent. It is efficient and accurate for fixed point problems. L.T. Watson, T.Y. Li, and C.Y. Wang have adapted the method for zero finding problems, the nonlinear complementarity problem, and nonlinear two-point boundary value problems. Here theoretical justification is given for applying the method to some mathematical programming problems, and computational results are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581630
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  • 7
    Electronic Resource
    Electronic Resource
    A finite characterization ofK-matrices in dimensions less than four (1986)
    Springer
    Mathematical programming 35 (1986), S. 17-31 
    Details
    ISSN: 1436-4646
    Keywords: Linear complementarity problem ; K-matrix ; Q 0-matrix ; finite characterization ; Q-matrix
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The class of realn × n matricesM, known asK-matrices, for which the linear complementarity problemw − Mz = q, w ≥ 0, z ≥ 0, w T z =0 has a solution wheneverw − Mz =q, w ≥ 0, z ≥ 0 has a solution is characterized for dimensionsn 〈4. The characterization is finite and ‘practical’. Several necessary conditions, sufficient conditions, and counterexamples pertaining toK-matrices are also given. A finite characterization of completelyK-matrices (K-matrices all of whose principal submatrices are alsoK-matrices) is proved for dimensions 〈4.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589438
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  • 8
    Electronic Resource
    Electronic Resource
    CP-rays in simplicial cones (1990)
    Springer
    Mathematical programming 48 (1990), S. 387-414 
    Details
    ISSN: 1436-4646
    Keywords: Simplicial cones ; faces ; orthogonal projections ; CP-points and rays ; linear complementarity problem ; positive definite matrices ; Z-matrices ; P-matrices
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract An interior point of a triangle is calledCP-point if its orthogonal projection on the line containing each side lies in the relative interior of that side. In classical mathematics, interest in the concept of regularity of a triangle is mainly centered on the property of every interior point of the triangle being a CP-point. We generalize the concept of regularity using this property, and extend this work to simplicial cones in ℝ n , and derive necessary and sufficient conditions for this property to hold in them. These conditions highlight the geometric properties of Z-matrices. We show that these concepts have important ramifications in algorithmic studies of the linear complementarity problem. We relate our results to other well known properties of square matrices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582265
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    Micropolar flow past a stretching sheet (1985)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 36 (1985), S. 845-853 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Résumé Nous étudions l'écoulement d'un fluid micropolaire et incompressible, de densité constante, le long d'une surface qui l'étend. Les équations de la couche limite qui régissent l'écoulement sont résolues numériquement. On utilise un algorithme quasi-Newtonien de type ≪least change secant update≫ avec une méthode homotopique /`a convergence globale. Certains résultats intéressants sont discutés et illustrés graphiquement.
    Notes: Summary This paper studies the flow of an incompressible, constant density micropolar fluid past a stretching sheet. The governing boundary layer equations of the flow are solved numerically using a globally convergent homotopy method in conjunction with a least change secant update quasi-Newton algorithm. The flow pattern depends on three non-dimensional parameters. Some interesting results are illustrated graphically and discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00944898
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    Paper (German National Licenses)
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  • 10
    Electronic Resource
    Electronic Resource
    Globally convergent homotopy algorithms for nonlinear systems of equations (1990)
    Springer
    Nonlinear dynamics 1 (1990), S. 143-191 
    Details
    ISSN: 1573-269X
    Keywords: Nonlinear systems ; homotopy algorithm ; globally convergent ; probability-one homotopy ; path tracking ; continuation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Probability-one homotopy methods are a class of algorithms for solving nonlinear systems of equations that are accurate, robust, and converge from an arbitrary starting point almost surely. These new globally convergent homotopy techniques have been successfully applied to solve Brouwer fixed point problems, polynomial systems of equations, constrained and unconstrained optimization problems, discretizations of nonlinear two-point boundary value problems based on shooting, finite differences, collocation, and finite elements, and finite difference, collocation, and Galerkin approximations to nonlinear partial differential equations. This paper introduces, in a tutorial fashion, the theory of globally convergent homotopy algorithms, deseribes some computer algorithms and mathematical software, and presents several nontrivial engineering applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01857785
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