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  • 1
    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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  • 2
    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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