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Multivariate Birkhoff interpolation [electronic resource] / Rudolph A. Lorentz

Author
Lorentz, Rudoph A.
Published
Berlin : New York : Springer-Verlag, [1992]
Copyright Date
©1992
Physical Description
ix, 192 pages : illustrations ; 25 cm.
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Contents
Machine generated contents note: 2.Univariate Interpolation -- 2.1.Introduction and definitions -- 2.2.Main theorems -- 3.Basic Properties of Birkhoff interpolation -- 3.1.Introduction and definitions -- 3.2.Properties of the spaces P[subscript s] -- 3.3.The Polya condition -- 3.4.Regular incidence matrices -- 3.5.Properties of the determinant -- 4.Singular Interpolation Schemes -- 4.1.Introduction and definitions -- 4.2.Hermite interpolation of type total degree in R[superscript d] -- 4.3.Uniform Hermite interpolation of type total degree in R[superscript 2], R[superscript 3], and R[superscript 4] -- 4.4.Hermite interpolation of tensor-product type -- 4.5.Number-theoretic considerations -- 4.6.Numerical results -- 4.7.Slicing the pie the other way -- 5.Shifts and Coalescences -- 5.1.Taylor expansion of the Vandermonde determinant -- 5.2.Definition of shifts -- 5.3.Existence of shifts -- 5.4.Numbers of shifts -- 5.5.Coefficients of the Taylor expansion -- 5.6.Coalescences -- 6.Decomposition Theorems -- 6.1.Introduction -- 6.2.Decomposition theorems without knots -- 6.3.Decomposition theorems with nodes -- 6.4.Comparison with other approaches -- 7.Reduction -- 7.1.Introduction -- 7.2.The reduction theorem -- 8.Examples -- 8.1.Introduction -- 8.2.Interpolation on rectangles -- 8.3.Triangular elements -- 9.Uniform Hermite Interpolation of Tensor-product Type -- 9.1.Introduction -- 9.2.The Polya condition -- 9.3.Basic theorems -- 9.4.Application of the basic theorems -- 9.5.Interpolation with derivatives of low order -- 9.6.Non-uniform Hermite interpolation of tensor-product type -- 10.Uniform Hermite Interpolation of Type Total Degree -- 10.1.Introduction -- 10.2.The Polya condition -- 10.3.Number-theoretic considerations -- 10.4.Interpolation and singularities -- 10.5.Minimality of triangles -- 10.6.An extension theorem -- 10.7.Interpolation of first derivatives -- 10.8.Interpolation of second and third derivatives -- 10.9.An interpolation in R[superscript 3] -- 10.10.A conjecture -- 10.11.An alternate proof of almost regularity for [actual symbol not reproducible] -- 10.12.The general case -- 11.Vandermonde determinants -- 11.1.Introduction -- 11.2.The determinant of Lagrange interpolation -- 11.3.Determinants of the decomposition theorem -- 11.4.Related results -- 11.5.Hack's interpolation scheme -- 11.6.Determinants of two particular problems -- 12.A theorem of Severi -- 12.1.Introduction and the theorem of Severi -- 12.2.Smaller interpolation spaces -- 12.3.Lagrange Interpolation -- 13.Kergin Interpolation via Birkhoff Interpolation -- 13.1.Introduction -- 13.2.Kergin's interpolant -- 13.3.An alternative proof of regularity -- A Appendix - A Bibliography on Multivariate Interpolation.
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ISBN
0387558705 (New York : acid-free paper)
3540558705 (Berlin : acid-free paper)
Bibliography Note
Includes bibliographical references (pages [171]-189).
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