DOI: 10.1007/bf01893414. Interpolation of scattered data: Distance matrices and conditionally positive definite functions

Interpolation of scattered data: Distance matrices and conditionally positive definite functions

10.1007/bf01893414

Crossref journal-article

Springer Science and Business Media LLC

Constructive Approximation (297)

Bibliography

Micchelli, C. A. (1986). Interpolation of scattered data: Distance matrices and conditionally positive definite functions. Constructive Approximation, 2(1), 11â22.

Authors 1

Charles A. Micchelli (first)

References 32 Referenced 1,103

M. Abramowitz, I. A. Stegun (1966): Handbook of Mathematical Functions (National Bureau of Standards Applied Mathematics Series 55). Washington, D.C.: National Bureau of Standards. / Handbook of Mathematical Functions (National Bureau of Standards Applied Mathematics Series 55) by M. Abramowitz (1966)
F. P. Agterberg (1974): Geomathematics. Amsterdam: Elsevier. / Geomathematics by F. P. Agterberg (1974)
N. Aronszajn (1950):Theory of reproducing kernels. Trans. Amer. Math. Soc.,68:337–404. (10.1090/S0002-9947-1950-0051437-7) / Trans. Amer. Math. Soc. by N. Aronszajn (1950)
R. Askey (1973): Radial Characteristic Functions (MRC Technical Sum: Report no. 1262). University of Wisconsin.
R. Barnhill, S. Stead (1983):Multistage trivariate surfaces. Preprint. (10.1216/RMJ-1984-14-1-103)
Blumenthal (1970): Theory and Application of Distance Geometry. New York: Chelsea Publishing. / Theory and Application of Distance Geometry by Blumenthal (1970)
W. F. Donoghue (1974): Monotone Matrix Functions and Analytic Continuation. Berlin Heidelberg New York: Springer-Verlag. (10.1007/978-3-642-65755-9) / Monotone Matrix Functions and Analytic Continuation by W. F. Donoghue (1974)
J. Duchon (1976):Splines minimizing rotation-invariant semi-norms in Sobolev spaces. In: Constructive Theory of Functions of Several Variables (W. Schempp, K. Zeller, eds.). Berlin Heidelberg New York: Springer-Verlag. / Constructive Theory of Functions of Several Variables by J. Duchon (1976)
N. Dyn, D. Levin, S. Rippa (1983):Numerical procedures for global surface smoothing of noisy scattered data. Preprint.
R. Franke (1982):Scattered data interpolation: tests of some methods. Math. Comp.,38:381–200. / Math. Comp. by R. Franke (1982)
R. Franke (1983):Lecture notes on global basis function methods for scattered data. International Symposium on Surface Approximation, University of Milano, Govgano, Italy. / Lecture notes on global basis function methods for scattered data by R. Franke (1983)
G. Gasper (1975):Positivity and special functions. In: The Theory and Application of Special Functions (R. Askey, ed.). New York: Academic Press. / The Theory and Application of Special Functions by G. Gasper (1975)
I. M. Gelfand, N. Ya. Vilenkin (1964): Generalized Functions, Vol. 4. New York: Academic Press. / Generalized Functions, Vol. 4 by I. M. Gelfand (1964)
R. L. Hardy (1971):Multiquadric equations of topography and other irregular surfaces. J. Geophys. Res., C. (10.1029/JB076i008p01905)
R. L. Hardy (1982):Surface fitting with biharmonic and harmonic models. In: Proceedings of the NASA Workshop on Surface Fitting. College Station, Texas: Center for Approximation Theory, Texas A & M University, pp. 136–146. / Surface fitting with biharmonic and harmonic models by R. L. Hardy (1982)
S. Helgason (1980): The Radon Transform. Basel: Birkhäuser. (10.1007/978-1-4899-6765-7) / The Radon Transform by S. Helgason (1980)
J. V. Linnik (1953):Linear forms and statical criteria, II. Ukrain. Mat. Zh.,51:247–290 [also (1962): Selected Translations in Mathematical Statistics and Probability, Vol. 5. Providence: American Mathematical Society, pp. 41–90]. / Ukrain. Mat. Zh. by J. V. Linnik (1953)
E. Luckas (1970): Characteristic Functions. New York: Hafner. / Characteristic Functions by E. Luckas (1970)
G. Matheron (1973):The intrinsic random functions and their applications. Adv. in Appl. Probab.,5:439–468. (10.2307/1425829) / Adv. in Appl. Probab. by G. Matheron (1973)
G. Matheron (1981):Splines and kriging: their formal equivalence. In: Syracuse University Geology Contribution 8 (D. F. Marriam, ed.). Syracuse, New York: Department of Geology, Syracuse University. / Syracuse University Geology Contribution 8 by G. Matheron (1981)
J. Meinguet (1979):An intrinsic approach to multivariate spline interpolation at arbitrary points. In: Polynomial and Splines Approximation (B. N. Sahney, ed.). Dordrecht: D. Reidel, pp. 163–190. (10.1007/978-94-009-9443-0_12) / Polynomial and Splines Approximation by J. Meinguet (1979)
J. von Neumann, I. J. Schoenberg (1941):Fourier integrals and metric geometry. Trans. Amer. Math. Soc.,50:226–251. (10.1090/S0002-9947-1941-0004644-8) / Trans. Amer. Math. Soc. by J. Neumann von (1941)
K. Salkauskas (1982):Some relationships between surface splines and kriging. In: Multivariate Approximation Theory II (W. Schempp, K. Zeller, eds.). Basel: Birkhäuser, pp. 313–325. (10.1007/978-3-0348-7189-1_25) / Multivariate Approximation Theory II by K. Salkauskas (1982)
I. P. Schagen (1979):Interpolation in two dimensions — a new technique. J. Inst. Math. Appl.,23:53–59. (10.1093/imamat/23.1.53) / J. Inst. Math. Appl. by I. P. Schagen (1979)
I. J. Schoenberg (1935):Remarks to Maurice Frechet's article “Sur la definition axiomatique d'une classe d'espace distancies vectoriellemment applicable sur l'espace de Hilbert.” Ann. of Math.,36:724–732. (10.2307/1968654) / Ann. of Math. by I. J. Schoenberg (1935)
I. J. Schoenberg (1938):Metric spaces and positive definite functions. Trans. Amer. Math. Soc.,44:522–536. (10.1090/S0002-9947-1938-1501980-0) / Trans. Amer. Math. Soc. by I. J. Schoenberg (1938)
I. J. Schoenberg (1938):Metric spaces and completely monotone functions. Ann. of Math.,39:811–841. (10.2307/1968466) / Ann. of Math. by I. J. Schoenberg (1938)
J. Stewart (1976):Positive definite functions and generalizations, an historical survey. Rocky Mountain J. Math.,6:409–434. (10.1216/RMJ-1976-6-3-409) / Rocky Mountain J. Math. by J. Stewart (1976)
Wahba (1982): Private communication.
G. N. Watson (1966): Theory of Bessel Functions, 2nd ed. Cambridge: Cambridge University Press. / Theory of Bessel Functions by G. N. Watson (1966)
D. V. Widder (1946): The Laplace Transform. Princeton: Princeton University Press. / The Laplace Transform by D. V. Widder (1946)
R. E. Williamson (1956):Multiply monotone functions and their Laplace transform. Duke Math. J.,23:189–207. (10.1215/S0012-7094-56-02317-1) / Duke Math. J. by R. E. Williamson (1956)

Dates

Type	When
Created	20 years, 1 month ago (July 5, 2005, 10:42 a.m.)
Deposited	5 years, 4 months ago (April 8, 2020, 12:32 a.m.)
Indexed	3 weeks ago (Aug. 7, 2025, 4:54 a.m.)
Issued	38 years, 8 months ago (Dec. 1, 1986)
Published	38 years, 8 months ago (Dec. 1, 1986)
Published Print	38 years, 8 months ago (Dec. 1, 1986)

Funders 0

None

BibTeX

@article{Micchelli_1986, title={Interpolation of scattered data: Distance matrices and conditionally positive definite functions}, volume={2}, ISSN={1432-0940}, url={http://dx.doi.org/10.1007/bf01893414}, DOI={10.1007/bf01893414}, number={1}, journal={Constructive Approximation}, publisher={Springer Science and Business Media LLC}, author={Micchelli, Charles A.}, year={1986}, month=dec, pages={11–22} }

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