DOI: 10.1090/s0025-5718-1990-0993931-7. Multivariate interpolation and conditionally positive definite functions. II

Multivariate interpolation and conditionally positive definite functions. II

10.1090/s0025-5718-1990-0993931-7

Crossref journal-article

American Mathematical Society (AMS)

Mathematics of Computation (14)

Abstract

We continue an earlier study of certain spaces that provide a variational framework for multivariate interpolation. Using the Fourier transform to analyze these spaces, we obtain error estimates of arbitrarily high order for a class of interpolation methods that includes multiquadrics.

Bibliography

Madych, W. R., & Nelson, S. A. (1990). Multivariate interpolation and conditionally positive definite functions. II. Mathematics of Computation, 54(189), 211â230. Portico.

Authors 2

W. R. Madych (first)
S. A. Nelson (additional)

References 11 Referenced 309

{'key': '1', 'volume-title': 'The theory of splines and their applications', 'author': 'Ahlberg, J. H.', 'year': '1967'} / The theory of splines and their applications by Ahlberg, J. H. (1967)
10.5802/aif.116 / Ann. Inst. Fourier (Grenoble) / Theory of Bessel potentials. I by Aronszajn, N. (1961)
{'key': '3', 'first-page': '33', 'article-title': 'Lebesgue spaces of differentiable functions and distributions', 'author': 'Calderón, A.-P.', 'year': '1961'} / Lebesgue spaces of differentiable functions and distributions by Calderón, A.-P. (1961)
W. F. Donoghue, Distributions and Fourier transforms, Academic Press, New York, 1969.
{'key': '5', 'first-page': '85', 'article-title': 'Splines minimizing rotation-invariant semi-norms in Sobolev spaces', 'author': 'Duchon, Jean', 'year': '1977'} / Splines minimizing rotation-invariant semi-norms in Sobolev spaces by Duchon, Jean (1977)
10.1051/m2an/1978120403251 / RAIRO Anal. Num\'{e}r. / Sur l’erreur d’interpolation des fonctions de plusieurs variables par les 𝐷^{𝑚}-splines by Duchon, Jean (1978)
{'key': '7', 'volume-title': 'Generalized functions. Vol. 1', 'author': 'Gel′fand, I. M.', 'year': '1964'} / Generalized functions. Vol. 1 by Gel′fand, I. M. (1964)
10.1007/BF02547758 / Acta Math. / Contribution à l’étude des fonctions dérivables d’une variable réelle by Gorny, A. (1939)
10.1007/978-3-662-41914-4 / Linear topological spaces / The University Series in Higher Mathematics by Kelley, J. L. (1963)
{'issue': '4', 'key': '10', 'first-page': '77', 'article-title': 'Multivariate interpolation and conditionally positive definite functions', 'volume': '4', 'author': 'Madych, W. R.', 'year': '1988', 'journal-title': 'Approx. Theory Appl.', 'ISSN': 'http://id.crossref.org/issn/1000-9221', 'issn-type': 'print'} / Approx. Theory Appl. / Multivariate interpolation and conditionally positive definite functions by Madych, W. R. (1988)
10.1007/978-3-642-99970-3 / Analytic inequalities / Die Grundlehren der mathematischen Wissenschaften, Band 165 by Mitrinović, D. S. (1970)

Dates

Type	When
Created	15 years, 2 months ago (June 28, 2010, 2:08 p.m.)
Deposited	3 years, 10 months ago (Nov. 2, 2021, 5:32 p.m.)
Indexed	3 weeks, 1 day ago (Aug. 12, 2025, 5:58 p.m.)
Issued	35 years, 8 months ago (Jan. 1, 1990)
Published	35 years, 8 months ago (Jan. 1, 1990)
Published Online	35 years, 8 months ago (Jan. 1, 1990)

Funders 0

None

BibTeX

@article{Madych_1990, title={Multivariate interpolation and conditionally positive definite functions. II}, volume={54}, ISSN={1088-6842}, url={http://dx.doi.org/10.1090/s0025-5718-1990-0993931-7}, DOI={10.1090/s0025-5718-1990-0993931-7}, number={189}, journal={Mathematics of Computation}, publisher={American Mathematical Society (AMS)}, author={Madych, W. R. and Nelson, S. A.}, year={1990}, pages={211–230} }

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