The Rayleigh quotient and dynamic programming
The purpose of this paper is to derive a nonlinear partial differential equation for which λ given by (1.3), is one value of the solution. In Section 2, we derive this equation using a straightforward dynamic programming approach. In Section 3, we discuss some computational aspects of derermining th...
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| Format: | Article |
| Language: | English |
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Wiley
1978-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S016117127800040X |
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| _version_ | 1832563282863456256 |
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| author | Richard Bellman |
| author_facet | Richard Bellman |
| author_sort | Richard Bellman |
| collection | DOAJ |
| description | The purpose of this paper is to derive a nonlinear partial differential equation for which λ given by (1.3), is one value of the solution. In Section 2, we derive this equation using a straightforward dynamic programming approach. In Section 3, we discuss some computational aspects of derermining the solution of this equation. In Section 4, we show that the same method may be applied to the nonlinear characteristic value problem. In Section 5, we discuss how the method may by applied to find the higher characteristic values. In Section 5, we discuss how the same method may be applied to some matrix problems. Finally, in Section 7, we discuss selective computation. |
| format | Article |
| id | doaj-art-3c02663b01244913840d7844712d90fc |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1978-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3c02663b01244913840d7844712d90fc2025-02-03T01:20:30ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251978-01-011440140510.1155/S016117127800040XThe Rayleigh quotient and dynamic programmingRichard Bellman0Department of Mathematics, Electrical Engineering, and Medicine, University of Southern California, Los Angeles 90007, California, USAThe purpose of this paper is to derive a nonlinear partial differential equation for which λ given by (1.3), is one value of the solution. In Section 2, we derive this equation using a straightforward dynamic programming approach. In Section 3, we discuss some computational aspects of derermining the solution of this equation. In Section 4, we show that the same method may be applied to the nonlinear characteristic value problem. In Section 5, we discuss how the method may by applied to find the higher characteristic values. In Section 5, we discuss how the same method may be applied to some matrix problems. Finally, in Section 7, we discuss selective computation.http://dx.doi.org/10.1155/S016117127800040XRayleigh quotientand dynamic programming. |
| spellingShingle | Richard Bellman The Rayleigh quotient and dynamic programming International Journal of Mathematics and Mathematical Sciences Rayleigh quotient and dynamic programming. |
| title | The Rayleigh quotient and dynamic programming |
| title_full | The Rayleigh quotient and dynamic programming |
| title_fullStr | The Rayleigh quotient and dynamic programming |
| title_full_unstemmed | The Rayleigh quotient and dynamic programming |
| title_short | The Rayleigh quotient and dynamic programming |
| title_sort | rayleigh quotient and dynamic programming |
| topic | Rayleigh quotient and dynamic programming. |
| url | http://dx.doi.org/10.1155/S016117127800040X |
| work_keys_str_mv | AT richardbellman therayleighquotientanddynamicprogramming AT richardbellman rayleighquotientanddynamicprogramming |