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  • 1
    Electronic Resource
    Electronic Resource
    Approximation by functions having restricted ranges: Equality case (1969)
    Springer
    Numerische Mathematik 14 (1969), S. 71-78 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper an alternation theorem is developed for approximating with functions having restricted ranges where equality is allowed to occur between the restraining curves.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02165100
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Judicial Review of Improper Purposes and Irrelevant Considerations (1976)
    Cambridge : Cambridge University Press
    The @Cambridge law journal 35 (1976), S. 272-291 
    Details
    ISSN: 0008-1973
    Source: Cambridge Journals Digital Archives
    Topics: Law
    Notes: Control of the abuse of discretion is arguably the central and most controversial part of judicial review of administrative action. Within abuse of discretion, review of improper purposes is probably the most difficult ground to define and expound. It is not seen easily as a separate and unique concept. There is no clear approach to it as a mechanism of review. On the other hand, review for the consideration of irrelevant factors appears to offer greater certainty. There has been, therefore, a tendency to bring both grounds together in terms of the latter. As a result, the line between improper purposes and irrelevant considerations has become blurred, and often they are seen as identical. A number of questions arise from this. Are the two grounds of review different? What is their content? How are they to be manipulated? Is the apparently expansive import of Padfield v. Minister of Agriculture, Fisheries and Food a significant development? If so, is it a shift in the right direction? Problems in review for abuse of discretion stem from several sources. The problems compound one another in a context of limited legal structures and judicial analysis. Abuse of discretion is too easily regarded as a “grab-bag” from which a ground of review can always be found to suit the conclusion sought to be reached on the merits. Judicial review is a flexible tool but each ground has a limited use. “Improper purposes” and “irrelevant factors” exist as distinct phrases because each represents a separate mode of analysis which is particularly useful in a given situation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1017/S0008197300012034
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A Chebyshev spectral method for boundary-layer models (1984)
    Springer
    Meteorology and atmospheric physics 33 (1984), S. 117-126 
    Details
    ISSN: 1436-5065
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geography , Physics
    Description / Table of Contents: Zusammenfassung Grenzschichten in der Atmosphäre und im Ozean nehmen oftmals die Struktur einer Mischungsschicht an, die von einer seichten, höchst stabilen Region begrenzt ist. Die Simulierung der Bewegung einer derartigen, stabilen Region stellt hohe Anforderungen an die numerische Modellierung. In dieser Arbeit wird die Anwendung der Chebyshevschen Spektralmethode untersucht. Wir vergleichen die Resultate von spektralen und endlichen Differenzenmethoden für ein einfaches, eindimensionales Testproblem mit bekannter, analytischer Lösung. Die Resultate zeigen die Zweckmäßigkeit der Spektral-methode zur Erreichung von genauen Lösungen von Grenzschichtproblemen auf.
    Notes: Summary Boundary-layers in the atmosphere and ocean often take on the structure of mixed layers bounded by narrow, highly stable regions. Simulation of the movement of such stable regions is a challenging task for the numerical modeler. Here we explore the use of Chebyshev spectral methods. We compare the results of spectral and finite difference methods for a simple one-dimensional test problem with known analytic solution. The results indicate the usefulness of the spectral method in obtaining accurate solutions to boundary-layer problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02257719
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Approximation and interpolation by convexity-preserving rational splines (1994)
    Springer
    Constructive approximation 10 (1994), S. 275-283 
    Details
    ISSN: 1432-0940
    Keywords: 65D07 ; 41A20 ; 41A29 ; Rational splines ; Data interpolation and approximation ; Convexity-preserving data fitting
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A discussion and algorithm for combined interpolation and approximation by convexity-preserving rational splines is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01263067
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  • 5
    Electronic Resource
    Electronic Resource
    Infinite-interval nonlinear approximations (1988)
    Springer
    Constructive approximation 4 (1988), S. 211-221 
    Details
    ISSN: 1432-0940
    Keywords: 41A46 ; Nonlinear uniform approximation ; Uniform approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Uniform nonlinear approximation on an infinite interval is studied. This study was motivated by a specific nonlinear approximation problem arising in the construction of a stiff ordinary differential equation system solver. General results include characterization, uniqueness, and discretization theorems, as well as a computational algorithm for this problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02075459
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Vectorial approximation by restricted rationals (1969)
    Springer
    Theory of computing systems 3 (1969), S. 232-243 
    Details
    ISSN: 1433-0490
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01703922
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    An ODE-based approach to nonlinearly constrained minimax problems (1995)
    Springer
    Numerical algorithms 9 (1995), S. 25-37 
    Details
    ISSN: 1572-9265
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider the following problem: Choosex 1, ...,x n to wherem 1,m 2,m 3 are integers with 0≤m 1≤m 2≤m 3, thef i are given real numbers, and theg i are given smooth functions. Constraints of the formg i (x 1, ...,x n )=0 can also be handled without problem. Each iteration of our algorithm involves approximately solving a certain non-linear system of first-order ordinary differential equations to get a search direction for a line search and using a Newton-like approach to correct back into the feasible region when necessary. The algorithm and our Fortran implementation of it will be discussed along with some examples. Our experience to date has been that the program is more robust than any of the library routines we have tried, although it generally requires more computer time. We have found this program to be an extremely useful tool in diverse areas, including polymer rheology, computer vision, and computation of convexity-preserving rational splines.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02143925
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Uniform rational approximation on large data sets (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1569-1575 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We report on a very effective program for uniform approximation of functions (or discrete data) by generalized rational functions of any number of variables over point sets so large that conventional methods are inapplicable. The points need not be arranged in a regular pattern, but if they are, the number of points is normally limited only by the computer time available. The program extends the differential correction algorithm discussed in an earlier article in this journal by combining it with a first Remes-type exchange procedure, while retaining the flexibility and robustness of differential correction. Furthermore, this algorithm is guaranteed to converge in theory. Testing has shown that, even when the point set is small enough for differential correction to be applied directly, this algorithm is usually faster. We discuss the algorithm and program along with several numerical examples, one of which involves more than three million data points. A FORTRAN listing with illustrative output can be obtained from the first author.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620181011
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    Uniform rational approximation of functions of several variables (1975)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 9 (1975), S. 297-323 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present a program which has given excellent results for uniform approximation of functions by polynomials, rational functions, generalized polynomials, and generalized rational functions. The algorithm is described in detail and several examples are discussed. The approximation is done over a finite point set, which is commonly a set of real numbers or points in the plane (in the latter case we are doing what is often known as surface fitting). Input to and output from the program is in tabular form. The method used is a linear programming approach known as the differential correction algorithm, which has been shown by several authors to always converge in theory (quadratically in some situations). In practice, we have obtained convergence in nearly every case, and quadratic convergence in most cases. The program can also be used for simultaneous approximation of several functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620090204
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    Paper (German National Licenses)
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  • 10
    Electronic Resource
    Electronic Resource
    Adaptive l1-l2 curve fitting (1979)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 871-903 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In References 1 and 2, algorithms were introduced for adaptively computing smooth piecewise polynomial approximations using uniform, least-squars (l2) and restricted-range uniform approximations. This present paper introduces a FORTRAN program for computing smooth piecewise polynomial approximations to data and/or precise mathematical functions (in discrete form) which allows the user the option of using best l1 of best l2 approximations. (The l2 option of this newly developed l1-l2 adaptive curve-fitting package supersedes the code listed in Reference 1 for the old least-squares program.) In this paper, adaptive curve-fitting algorithm used in this l1-l2 package is described in detail, the FORTRAN program is the given (in the Appendix) and discussed, the numerical results are presented in an effort to illustrate how the l1 and l2 versions of this algorithm may be used most effectively.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620140608
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    Paper (German National Licenses)
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