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  • 1
    Electronic Resource
    Electronic Resource
    Hexagonal-columnar mesophases in substituted phthalocyaninatopolysiloxanes (1993)
    s.l. : American Chemical Society
    Macromolecules 26 (1993), S. 2057-2063 
    Details
    ISSN: 1520-5835
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ma00060a039
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  • 2
    Electronic Resource
    Electronic Resource
    Small-angle x-ray scattering from dilute solutions of substituted phthalocyaninato-polysiloxanes (1991)
    s.l. : American Chemical Society
    Macromolecules 24 (1991), S. 2240-2252 
    Details
    ISSN: 1520-5835
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ma00009a019
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  • 3
    Electronic Resource
    Electronic Resource
    Ein algorithmischer Zugang zu Polynomen und Splines (1996)
    Springer
    Mathematische Semesterberichte 43 (1996), S. 169-189 
    Details
    ISSN: 0720-728X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Zusammenfassung. Um polynomiale Kurven auf dem Computer modellieren zu können, verwendet man in der CAD-Praxis zumeist sogenannte Bézier-Kurven. Verallgemeinert man den zugehörigen Auswertungsalgorithmus, so kann man, auf ganz konstruktive Art auch Splinekurven definieren und ihre wesentlichen Eigenschaften auf sehr elementare Art und Weise herleiten. Der Zusammenhang wird dabei durch das sogenannte “Blossoming principle” hergestellt.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s005910050020
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  • 4
    Electronic Resource
    Electronic Resource
    Polynomial interpolation of minimal degree (1997)
    Springer
    Numerische Mathematik 78 (1997), S. 59-85 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 65D10, 41A05, 41A10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. Minimal degree interpolation spaces with respect to a finite set of points are subspaces of multivariate polynomials of least possible degree for which Lagrange interpolation with respect to the given points is uniquely solvable and degree reducing. This is a generalization of the concept of least interpolation introduced by de Boor and Ron. This paper investigates the behavior of Lagrange interpolation with respect to these spaces, giving a Newton interpolation method and a remainder formula for the error of interpolation. Moreover, a special minimal degree interpolation space will be introduced which is particularly beneficial from the numerical point of view.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050304
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  • 5
    Electronic Resource
    Electronic Resource
    Building refinable functions from their values at integers (2000)
    Springer
    Calcolo 37 (2000), S. 139-158 
    Details
    ISSN: 1126-5434
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract: In this paper we consider the problem of generating a refinable function from values specified at the integers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s100920070006
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  • 6
    Electronic Resource
    Electronic Resource
    Computational aspects of multivariate polynomial interpolation (1995)
    Springer
    Advances in computational mathematics 3 (1995), S. 219-237 
    Details
    ISSN: 1572-9044
    Keywords: Lagrange interpolation ; finite difference ; algorithm ; Primary ; 41A05 ; 41A10 ; 65D05 ; 65D10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The paper is concerned with the practical implementation of two methods to compute the solution of polynomial interpolation problems. In addition to a description of the implementation, practical results and several improvements will be discussed, focusing on speed and robustness of the algorithms under consideration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02432000
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  • 7
    Electronic Resource
    Electronic Resource
    Polynomial interpolation in several variables (2000)
    Springer
    Advances in computational mathematics 12 (2000), S. 377-410 
    Details
    ISSN: 1572-9044
    Keywords: interpolation ; multivariate polynomials ; Newton approach ; divided differences ; Gröbner bases ; H-bases
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This is a survey of the main results on multivariate polynomial interpolation in the last twenty-five years, a period of time when the subject experienced its most rapid development. The problem is considered from two different points of view: the construction of data points which allow unique interpolation for given interpolation spaces as well as the converse. In addition, one section is devoted to error formulas and another to connections with computer algebra. An extensive list of references is also included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018981505752
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  • 8
    Electronic Resource
    Electronic Resource
    H-bases for polynomial interpolation and system solving (2000)
    Springer
    Advances in computational mathematics 12 (2000), S. 335-362 
    Details
    ISSN: 1572-9044
    Keywords: ideal bases ; Gröbner bases ; multivariate polynomials ; interpolation ; systems of polynomial equations ; 65D05 ; 65H10 ; 13P10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The H-basis concept allows, similarly to the Gröbner basis concept, a reformulation of nonlinear problems in terms of linear algebra. We exhibit parallels of the two concepts, show properties of H-bases, discuss their construction and uniqueness questions, and prove that n polynomials in n variables are, under mild conditions, already H-bases. We apply H-bases to the solution of polynomial systems by the eigenmethod and to multivariate interpolation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018937723499
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  • 9
    Electronic Resource
    Electronic Resource
    On vector subdivision (1998)
    Springer
    Mathematische Zeitschrift 229 (1998), S. 621-674 
    Details
    ISSN: 0025-5874
    Keywords: Mathematics Subject Classification (1991): 65D10, 41A05, 41A10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. In this paper we give a complete characterization of the convergence of stationary vector subdivision schemes and the regularity of the associated limit function. These results extend and complete our earlier work on vector subdivision and its use in the construction of multiwavelets.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00004676
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  • 10
    Electronic Resource
    Electronic Resource
    Regularity of multiwavelets (1997)
    Springer
    Advances in computational mathematics 7 (1997), S. 455-545 
    Details
    ISSN: 1572-9044
    Keywords: subdivision ; refinable functions ; regularity ; multiwavelets ; 39B12 ; 41A15 ; 41A25 ; 65D99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The motivation for this paper is an interesting observation made by Plonka concerning the factorization of the matrix symbol associated with the refinement equation for B-splines with equally spaced multiple knots at integers and subsequent developments which relate this factorization to regularity of refinable vector fields over the real line. Our intention is to contribute to this train of ideas which is partially driven by the importance of refinable vector fields in the construction of multiwavelets. The use of subdivision methods will allow us to consider the problem almost entirely in the spatial domain and leads to exact characterizations of differentiability and Hölder regularity in arbitrary L p spaces. We first study the close relationship between vector subdivision schemes and a generalized notion of scalar subdivision schemes based on bi-infinite matrices with certain periodicity properties. For the latter type of subdivision scheme we will derive criteria for convergence and Hölder regularity of the limit function, which mainly depend on the spectral radius of a bi-infinite matrix induced by the subdivision operator, and we will show that differentiability of the limit functions can be characterized by factorization properties of the subdivision operator. By switching back to vector subdivision we will transfer these results to refinable vectors fields and obtain characterizations of regularity by factorization and spectral radius properties of the symbol associated to the refinable vector field. Finally, we point out how multiwavelets can be generated from orthonormal refinable bi-infinite vector fields.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018971524949
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