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Numerical Analysis: Quasilinearization and the estimation of differential operators from eigenvalues

Authors:

R. E. Bellman,

H. H. Kagiwada,

R. E. Kalaba,

R. VasudevanAuthors Info & Claims

Communications of the ACM, Volume 11, Issue 4

Pages 255 - 256

https://doi.org/10.1145/362991.363007

Published: 01 April 1968 Publication History

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Abstract

Given a linear ordinary differential operator containing several unknown constants and a number of its eigenvalues, the values of the unknown constants are estimated. A precise formulation is provided, and an effective numerical procedure for solution is indicated. The results of some computational experiments are given.

References

[1]

BELLMAN, R. E., KAGIWADA, H. H., AND KALABA, R. E. Quasilinearization and the calculation of eigenvalues. Comm. ACM 9, 7 (July 1966), 522-524.

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[2]

BELLMAN, Pt. E., AND KALABA, R.E. Quasilinearizalion and Nonlinear Boundary-Value Problems. American Elsevier, New York, 1965.

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[3]

WILSON, E., DECIUS, J., AND CROSS, F. Molecular Vibrations. McGraw-Hill, New York, 1955, Ch. 8.

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[4]

AMBARZUMIAN, V. Uber eine Frage der Eigenwerttheorie. Zeit. Phys. 53 (1929), 690-695.

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[5]

KAGIWADA, H. Computational aspects of inverse problems in analytical mechanics, transport theory, and wave propagation. Ph.D. Thesis, U. of Kyoto, 1965; also RM-4549- ARPA, The RAND Corp., Santa Monica, Calif., Aug. 1965.

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Lew A(1986)Richard Bellman's contributions to computer scienceJournal of Mathematical Analysis and Applications10.1016/0022-247X(86)90146-0119:1-2(90-96)Online publication date: Oct-1986
https://doi.org/10.1016/0022-247X(86)90146-0
Roth R(1981)Techniques in the identification of deterministic systemsIEEE Transactions on Automatic Control10.1109/TAC.1981.110278626:5(1169-1176)Online publication date: Oct-1981
https://doi.org/10.1109/TAC.1981.1102786
(1970)BIBLIOGRAPHYIterative Solution of Nonlinear Equations in Several Variables10.1016/B978-0-12-528550-6.50029-6(523-557)Online publication date: 1970
https://doi.org/10.1016/B978-0-12-528550-6.50029-6

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Published In

Communications of the ACM Volume 11, Issue 4

April 1968

65 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/362991

Editor:
Gerard Salton
Cornell Univ. Ithaca, NY

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 April 1968

Published in CACM Volume 11, Issue 4

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Lew A(1986)Richard Bellman's contributions to computer scienceJournal of Mathematical Analysis and Applications10.1016/0022-247X(86)90146-0119:1-2(90-96)Online publication date: Oct-1986
https://doi.org/10.1016/0022-247X(86)90146-0
Roth R(1981)Techniques in the identification of deterministic systemsIEEE Transactions on Automatic Control10.1109/TAC.1981.110278626:5(1169-1176)Online publication date: Oct-1981
https://doi.org/10.1109/TAC.1981.1102786
(1970)BIBLIOGRAPHYIterative Solution of Nonlinear Equations in Several Variables10.1016/B978-0-12-528550-6.50029-6(523-557)Online publication date: 1970
https://doi.org/10.1016/B978-0-12-528550-6.50029-6

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References

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Haar wavelet-quasilinearization technique for fractional nonlinear differential equations

Quasilinearization Method for Nonlinear Elliptic Boundary-Value Problems

A numerical method based on Legendre wavelet and quasilinearization technique for fractional Lane-Emden type equations

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