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pro vyhledávání: '"Richard J. Fateman"'
Autor:
Richard J. Fateman
Publikováno v:
ACM Communications in Computer Algebra. 49:38-47
A popular technique to direct transformations of algebraic expressions in a computer algebra system such as Macsyma/Maxima or Mathematica is to first write out a pattern or template for some expected class of "input" expressions and use a built-in sy
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fc7e0432746983847700a09174853832
https://doi.org/10.1145/2815111.2815112
https://doi.org/10.1145/2815111.2815112
Autor:
Richard J. Fateman
Publikováno v:
ACM Communications in Computer Algebra. 48:78-89
Algorithm differentiation (AD) is a technique used to transform a program F computing a numerical function of one argument F(x) into another program G(p) that returns a pair, hF(p), F0(p)i where by F0(p) we mean the derivative of F with respect to it
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2cf42454a3f6ad0978ead8552ad25475
https://doi.org/10.1145/2733693.2733696
https://doi.org/10.1145/2733693.2733696
Autor:
Richard J. Fateman
Publikováno v:
ACM SIGSAM Bulletin. 37:109-116
The speed of modern computers can be increased by organizing computations so that memory access patterns correspond more closely to the memory cache-loading patterns implemented in the hardware. Rearranging code and data are each possible. Here we co
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::558dcc5eceb6508e07cb5cbcf471ac51
https://doi.org/10.1145/968708.968711
https://doi.org/10.1145/968708.968711
Autor:
Richard J. Fateman
Publikováno v:
ACM SIGSAM Bulletin. 37:4-15
How should one design and implement a program for the multiplication of sparse polynomials? This is a simple question, necessarily addressed by the builders of any computer algebra system (CAS). To examine a few options we start with a single easily-
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::73fc767ca539f9befd224aa1200cc9f6
https://doi.org/10.1145/844076.844080
https://doi.org/10.1145/844076.844080
Autor:
Richard J. Fateman, William Kahan
Publikováno v:
ACM SIGSAM Bulletin. 33:7-28
Divided differences are enormously useful in developing stable and accurate numerical formulas. For example, programs to compute f ( x )- f ( y ) as might occur in integration, can be notoriously inaccurate. Such problems can be cured by approaching
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::4579e11f60e6e883b2888c4b82b2cba0
https://doi.org/10.1145/334714.334716
https://doi.org/10.1145/334714.334716
A short note on short differentiation programs in lisp, and a comment on lagarithmic differentiation
Autor:
Richard J. Fateman
Publikováno v:
ACM SIGSAM Bulletin. 32:2-7
By tradition and design, Lisp is alleged to be a particularly convenient programming language in which to represent algebraic expressions and in which to write a differentiation program. Over the years, most books on Lisp have included programs for d
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b69fbf6512c92a21adddec45fac9758a
https://doi.org/10.1145/307339.307341
https://doi.org/10.1145/307339.307341
Autor:
Richard J. Fateman
Publikováno v:
International Journal of Modern Physics C. :509-525
Using a classic example proposed by G. I. Taylor, we reconsider through the use of computer algebra, the mathematical analysis of a fundamental process in turbulent flow, namely: How do large scale eddies evolve into smaller scale ones to the point w
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7b46179fd036dcb6df7f4f0bf53b874f
https://doi.org/10.1142/s0129183198000418
https://doi.org/10.1142/s0129183198000418
Autor:
Richard J. Fateman
Publikováno v:
ACM SIGSAM Bulletin. 30:8-11
Among the basic equations one might wish a computer to solve symbolically is the inverse of the power function, solving y = z w for z. (Note: z w ≡ exp( w ln z )). While many special cases, easily solved, abound, the general question is fraught wit
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https://doi.org/10.1145/235699.235701
https://doi.org/10.1145/235699.235701
Publikováno v:
Journal of Visual Communication and Image Representation. 7:2-15
There is a wealth of mathematical knowledge that could be potentially very useful in many computational applications, but is not available in electronic form. This knowledge comes in the form of mechanically typeset books and journals going back more
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2d6228f05b66728b348a13445ed478fa
https://doi.org/10.1006/jvci.1996.0002
https://doi.org/10.1006/jvci.1996.0002
Autor:
Richard J. Fateman, Mark Hayden
Publikováno v:
ACM SIGSAM Bulletin. 30:25-30
Two techniques for speeding up a traditional Lisp-based symbolic manipulation system (Macsyma) were outlined in a previous paper [2]. These were: using unique representations for equivalent "kernel" expressions (where a kernel here is basically anyth
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::2acf390a50c5bebd2ec3971bf86f56c2
https://doi.org/10.1145/231191.231195
https://doi.org/10.1145/231191.231195