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A note on Tchakaloff's Theorem
Author(s):
Mihai
Putinar
Journal:
Proc. Amer. Math. Soc.
125
(1997),
2409-2414.
MSC (1991):
Primary 65D32, 44A60
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Abstract:
A classical result of Tchakaloff on the existence of exact quadrature formulae up to a given degree is extended to positive measures without compact support. A criterion for the existence of Gaussian quadratures for a class of such measures is also derived from the main proof.
References:
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- 2.
- Curto, R.E. and Fialkow, L., Flat extensions of positive moment matrices: relations in analytic or conjugate terms, preprint 1994.
- 3.
- Mysovskikh, I.P., On Chakalov's theorem, U.S.S.R. Comput. Math. and Math. Phys. 15(1975), no. 6, 221-227; (translation in Zh. Vychisl. Mat. i Mat. Fiz. 15(1975), no. 6, 1589-1593, 1627).
- 4.
- Mysovskikh, I.P., Interpolation cubature formulas (in Russian), Nauka, Moscow, 1981.
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- Reznick, B., Sums of even powers of real linear forms, Mem. Amer. Math. Soc. No. 463, Amer. Math. Soc., Providence, R.I., 1992. MR 93h:11043
- 6.
- Stroud, A.H., Approximate Calculation of Multiple Integrals, Prentice-Hall, Englewood Cliffs, New Jersey, 1971. MR 48:5348
- 7.
- Schmid, H.J., Interpolatorische Kubaturformeln, Diss. Math. (Rozprawy Mat.) 220(1983), 122 pp. MR 85i:65034
- 8.
- Schmid, H.J., Two-dimensional minimal cubature formulas and matrix equations, SIAM J. Matrix Anal. Appl. 16(1995), 898-921. MR 96d:65050
- 9.
- Tchakaloff, V., Formules de cubature mécanique à coefficients non négatifs, Bull. Sci. Math. 81(1957), 123-134. MR 20:1145
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Additional Information:
Mihai
Putinar
Affiliation:
Department of Mathematics, University of California, Riverside, California 92521
Email:
mputinar@math.ucr.edu
DOI:
10.1090/S0002-9939-97-03862-8
PII:
S 0002-9939(97)03862-8
Received by editor(s):
January 16, 1996
Received by editor(s) in revised form:
February 22, 1996
Additional Notes:
This work was partially supported by the National Foundation Grant DMS 9500954
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1997,
American Mathematical Society
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