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  • 1
    Electronic Resource
    Electronic Resource
    Optimization theory in linear spaces. I (1969)
    Springer
    Mathematische Annalen 182 (1969), S. 189-206 
    Details
    ISSN: 1432-1807
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01350322
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  • 2
    Electronic Resource
    Electronic Resource
    High dimensional integration of smooth functions over cubes (1996)
    Springer
    Numerische Mathematik 75 (1996), S. 79-97 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 41A55, 41A63, 65D30, 65Y20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. We construct a new algorithm for the numerical integration of functions that are defined on a $d$ -dimensional cube. It is based on the Clenshaw-Curtis rule for $d=1$ and on Smolyak's construction. This way we make the best use of the smoothness properties of any (nonperiodic) function. We prove error bounds showing that our algorithm is almost optimal (up to logarithmic factors) for different classes of functions with bounded mixed derivative. Numerical results show that the new method is very competitive, in particular for smooth integrands and $d \ge 8$ .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050231
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  • 3
    Electronic Resource
    Electronic Resource
    On the rate of superlinear convergence of a class of variable metric methods (1980)
    Springer
    Numerische Mathematik 35 (1980), S. 293-313 
    Details
    ISSN: 0945-3245
    Keywords: AMS (MOS) ; 90C30 ; CR: 5.15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary This paper considers a class of variable metric methods for unconstrained minimization. Without requiring exact line searches each algorithm in this class converges globally and superlinearly on convex functions. Various results on the rate of the superlinear convergence are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01396414
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  • 4
    Electronic Resource
    Electronic Resource
    Methods of conjugate directions versus quasi-Newton methods (1972)
    Springer
    Mathematical programming 3 (1972), S. 101-116 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract It is shown that algorithms for minimizing an unconstrained functionF(x), x ∈ E n , which are solely methods of conjugate directions can be expected to exhibit only ann or (n−1) step superlinear rate of convergence to an isolated local minimizer. This is contrasted with quasi-Newton methods which can be expected to exhibit every step superlinear convergence. Similar statements about a quadratic rate of convergence hold when a Lipschitz condition is placed on the second derivatives ofF(x).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01584978
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  • 5
    Electronic Resource
    Electronic Resource
    A superlinearly convergent method for minimization problems with linear inequality constraints (1973)
    Springer
    Mathematical programming 4 (1973), S. 44-71 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A method is described for minimizing a continuously differentiable functionF(x) ofn variables subject to linear inequality constraints. It can be applied under the same general assumptions as any method of feasible directions. IfF(x) is twice continuously differentiable and the Hessian matrix ofF(x) has certain properties, then the algorithm generates a sequence of points which converges superlinearly to the unique minimizer ofF(x). No computation of secondorder derivatives is required.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01584646
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  • 6
    Electronic Resource
    Electronic Resource
    Average errors for zero finding: Lower bounds for smooth or monotone functions (1994)
    Springer
    Aequationes mathematicae 47 (1994), S. 120-120 
    Details
    ISSN: 1420-8903
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01838149
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  • 7
    Electronic Resource
    Electronic Resource
    Average errors for zero finding: Lower bounds for smooth or monotone functions (1994)
    Springer
    Aequationes mathematicae 48 (1994), S. 194-219 
    Details
    ISSN: 1420-8903
    Keywords: 65H05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We study zero finding for functions fromC r ([0, 1]) withf(0) ⋅f(1) 〈 0 and for monotone functions fromC([0, 1]). We show that a lower boundγ n with a constantγ holds for the average error of any method usingn function or derivative evaluations. Here the average is defined with respect to conditionalr-fold Wiemer measures or Ulam measures, and the error is understood in the root or residual sense. As in the worst case, we therefore cannot obtain superlinear convergence even for classes of smooth functions which have only simple zeros.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01832985
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  • 8
    Electronic Resource
    Electronic Resource
    Simple Cubature Formulas with High Polynomial Exactness (1999)
    Springer
    Constructive approximation 15 (1999), S. 499-522 
    Details
    ISSN: 1432-0940
    Keywords: Key words. Cubature formula, Polynomial exactness, Universality, Optimal error bounds, Fully symmetric formulas, Sparse grids, Interpolation. AMS Classification. 41A55, 41A63, 65D30, 65D32, 65Y20.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. We study cubature formulas for d -dimensional integrals with arbitrary weight function of tensor product form. We present a construction that yields a high polynomial exactness: for fixed degree, the number of knots depends on the dimension in an order-optimal way. The cubature formulas are universal: the order of convergence is almost optimal for two different scales of function spaces. The construction is simple: a small number of arithmetical operations is sufficient to compute the knots and the weights of the formulas.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s003659900119
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  • 9
    Electronic Resource
    Electronic Resource
    High dimensional polynomial interpolation on sparse grids (2000)
    Springer
    Advances in computational mathematics 12 (2000), S. 273-288 
    Details
    ISSN: 1572-9044
    Keywords: multivariate polynomial interpolation ; sparse grids ; least solution ; universal method ; tractability ; 41A05 ; 41A63 ; 65D05 ; 41A25
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study polynomial interpolation on a d-dimensional cube, where d is large. We suggest to use the least solution at sparse grids with the extrema of the Chebyshev polynomials. The polynomial exactness of this method is almost optimal. Our error bounds show that the method is universal, i.e., almost optimal for many different function spaces. We report on numerical experiments for d = 10 using up to 652 065 interpolation points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018977404843
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  • 10
    Electronic Resource
    Electronic Resource
    Sensibilisierte Photolyse von Bis(dimethylglyoximato)cobalt(III)-Komplexen mit axial koordiniertem Azid bzw. Thiophenolat als photochemischen OpferligandenHerrn Professor Lothar Beyer zum 60. Geburtstag gewidmet (1997)
    New York, NY : Wiley-Blackwell
    Journal für Praktische Chemie/Chemiker-Zeitung 339 (1997), S. 272-276 
    Details
    ISSN: 0941-1216
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Sensitized Photolysis of Bis(dimethylglyoximato)cobalt(III) Complexes with Axially Coordinated Azide or Thiophenolate as Photochemical Sacrificial LigandsThe photolysis of [N3Co(dmg)2pyr] 1a and [PhSCo(dmg)2pyr] 1b (dmg = dimethylglyoxime, pyr = pyridine) is sensitized by both [Ru(bpy)3]Cl2 2 (bpy = 2,2′-bipyridine) and Michler's thioketone 3 (4,4′-bis(dimethyl-amino)-thiobenzophenone). Quenching of 2 by the cobalt(III) chelates 1a and 1b was studied by luminescence spectroscopy. The quenching rate constants calculated are in the order of magnitude of kq ≅ 106 mol-1 s-1. Polychromatic irradiation (〉 250 nm) of 1b and 3 in the presence of thiophenole (PhSH) leads to hydrogen evolution, whereas long-wavelength (546 nm) irradiation does not. The results of these sensitization experiments support strongly a mechanism of catalyzed photolysis of PhSH as proposed earlier.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/prac.19973390148
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