Abstraction in Numerical Methods
We illustrate how the liberal use of high-order procedural abstractions and infinite streams helps us to express some of the vocabulary and methods of numerical analysis. We develop a software toolbox encapsulating the technique of Richardson extrapolation, and we apply these tools to the prob...
| Main Authors: | , |
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| Language: | en_US |
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2004
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| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/6060 |
| _version_ | 1826199273943859200 |
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| author | Halfant, Matthew Sussman, Gerald Jay |
| author_facet | Halfant, Matthew Sussman, Gerald Jay |
| author_sort | Halfant, Matthew |
| collection | MIT |
| description | We illustrate how the liberal use of high-order procedural abstractions and infinite streams helps us to express some of the vocabulary and methods of numerical analysis. We develop a software toolbox encapsulating the technique of Richardson extrapolation, and we apply these tools to the problems of numerical integration and differentiation. By separating the idea of Richardson extrapolation from its use in particular circumstances, we indicate how numerical programs can be written that exhibit the structure of the ideas from which they are formed. |
| first_indexed | 2024-09-23T11:17:11Z |
| id | mit-1721.1/6060 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:17:11Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | mit-1721.1/60602019-04-12T08:28:53Z Abstraction in Numerical Methods Halfant, Matthew Sussman, Gerald Jay SCHEME abstraction programming methodology Richardsonsextrapolation LISP We illustrate how the liberal use of high-order procedural abstractions and infinite streams helps us to express some of the vocabulary and methods of numerical analysis. We develop a software toolbox encapsulating the technique of Richardson extrapolation, and we apply these tools to the problems of numerical integration and differentiation. By separating the idea of Richardson extrapolation from its use in particular circumstances, we indicate how numerical programs can be written that exhibit the structure of the ideas from which they are formed. 2004-10-04T14:37:13Z 2004-10-04T14:37:13Z 1987-10-01 AIM-997 http://hdl.handle.net/1721.1/6060 en_US AIM-997 19 p. 2040493 bytes 819246 bytes application/postscript application/pdf application/postscript application/pdf |
| spellingShingle | SCHEME abstraction programming methodology Richardsonsextrapolation LISP Halfant, Matthew Sussman, Gerald Jay Abstraction in Numerical Methods |
| title | Abstraction in Numerical Methods |
| title_full | Abstraction in Numerical Methods |
| title_fullStr | Abstraction in Numerical Methods |
| title_full_unstemmed | Abstraction in Numerical Methods |
| title_short | Abstraction in Numerical Methods |
| title_sort | abstraction in numerical methods |
| topic | SCHEME abstraction programming methodology Richardsonsextrapolation LISP |
| url | http://hdl.handle.net/1721.1/6060 |
| work_keys_str_mv | AT halfantmatthew abstractioninnumericalmethods AT sussmangeraldjay abstractioninnumericalmethods |