ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    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
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    Ein Verfahren zur Lösung parameterabhängiger, nichtlinearer Maximum-Probleme (1962)
    Springer
    Mathematical methods of operations research 6 (1962), S. 149-166 
    Details
    ISSN: 1432-5217
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Summary In this paper parametric maximum problems are treated with the aim to represent the optimal solution explicitly as a function of the parameter. The method developped to this purpose permits to divide the given parameter interval uniquely into a finite number of subintervals in such a manner that it is possible to attach to each of these a system of equations depending from the parameter the solution of which corresponds with the optimal solution. These systems of equations are linear for maximum problems with quadratic object function and linear restrictions. Their solutions give the components of the optimal solution in the form of quotients of polynoms of the parameter. A further extension of this method enables the solution of quadratic maximum problems with strict concave object function and linear restrictions.
    Notes: Zusammenfassung Der Gegenstand dieser Arbeit ist die Behandlung parameterabhängiger Maximum-Probleme mit der Zielsetzung, die optimale Lösung explizit als Funktion des Parameters darzustellen. Zu diesem Zweck wird ein Verfahren entwickelt, das es gestattet, das vorgegebene Parameter-intervall eindeutig so in endlich viele Teilintervalle aufzuteilen, daß sich jedem Teilbereich ein vom Parameter abhängiges Gleichungssystem zuordnen läßt, dessen Lösung mit der optimalen Lösung übereinstimmt. Für Maximum-Probleme mit quadratischer Zielfunktion und linearen Nebenbedingungen sind diese Gleichungssysteme linear. Ihre Auflösung ergibt die Komponenten der optimalen Lösung in der Gestalt von Quotienten gebildet aus Polynomen des Parameters. Als eine Anwendung dieses Verfahrens erhält man eine Methode zur Lösung quadratischer Maximum-Probleme mit streng konkaver Zielfunktion und linearen Nebenbedingungen.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01920852
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...