Unrestricted algorithm: Difference between revisions
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| ⚫ | An '''unrestricted algorithm''' is an [[algorithm]] for the computation of a [[mathematical function]] that puts no restrictions on the range of the [[Argument (mathematics)|argument]] or on the precision that may be demanded in the result.<ref name="Clenshaw">{{cite journal|last1=C.W. Clenshaw and F. W. J. Olver|title=An unrestricted algorithm for the exponential function|journal=SIAM Journal on Numerical Analysis|date=April 1980|volume= 17|issue=2|pages=310–331|jstor=2156615}}</ref> The idea of such an algorithm was put forward by C. W. Clenshaw and F. W. J. Olver in a paper published in 1980.<ref name=Clenshaw/><ref name="Brent">{{cite book|last1=Richard P Brent|chapter=Unrestricted algorithms for elementary and special functions|title=Information Processing |volume=80 |editor=S. H. Lavington |publisher=North-Holland, Amsterdam|date=1980|pages=613–619|arxiv=1004.3621}}</ref> |
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| ⚫ | In the problem of developing algorithms for computing, as regards the values of a [[real-valued function]] of a [[real variable]] (e.g., ''g''[''x''] in "restricted" algorithms), the error that can be tolerated in the result is specified in advance. An interval on the [[real line]] would also be specified for values when the values of a function are to be evaluated. Different algorithms may have to be applied for evaluating functions outside the interval. An unrestricted algorithm envisages a situation in which a user may stipulate the value of ''x'' and also the precision required in ''g''(''x'') quite arbitrarily. The algorithm should then produce an acceptable result without failure.<ref name = Clenshaw/> |
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| ⚫ | An '''unrestricted algorithm''' is an [[algorithm]] for the computation of a mathematical function that puts no restrictions on the range of the argument or on the precision that may be demanded in the result.<ref name="Clenshaw">{{cite journal|last1=C.W. Clenshaw and F. W. J. Olver|title=An unrestricted algorithm for the exponential function|journal=SIAM Journal on Numerical Analysis|date=April 1980|volume= 17|issue=2|pages=310–331|jstor=2156615}}</ref> The idea of such an algorithm was put forward by C. W. Clenshaw and F. W. J. Olver in a paper published in 1980.<ref name=Clenshaw/><ref name="Brent">{{cite book|last1=Richard P Brent|chapter=Unrestricted algorithms for elementary and special functions|title=Information Processing |volume=80 |editor=S. H. Lavington |publisher=North-Holland, Amsterdam|date=1980|pages=613–619|arxiv=1004.3621}}</ref> |
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| ⚫ | In the problem of developing algorithms for computing the values of a real-valued function of a real variable |
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==References== |
==References== |
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Revision as of 08:12, 18 December 2018
An unrestricted algorithm is an algorithm for the computation of a mathematical function that puts no restrictions on the range of the argument or on the precision that may be demanded in the result.[1] The idea of such an algorithm was put forward by C. W. Clenshaw and F. W. J. Olver in a paper published in 1980.[1][2]
In the problem of developing algorithms for computing, as regards the values of a real-valued function of a real variable (e.g., g[x] in "restricted" algorithms), the error that can be tolerated in the result is specified in advance. An interval on the real line would also be specified for values when the values of a function are to be evaluated. Different algorithms may have to be applied for evaluating functions outside the interval. An unrestricted algorithm envisages a situation in which a user may stipulate the value of x and also the precision required in g(x) quite arbitrarily. The algorithm should then produce an acceptable result without failure.[1]
References
- ^ a b c C.W. Clenshaw and F. W. J. Olver (April 1980). "An unrestricted algorithm for the exponential function". SIAM Journal on Numerical Analysis. 17 (2): 310–331. JSTOR 2156615.
- ^ Richard P Brent (1980). "Unrestricted algorithms for elementary and special functions". In S. H. Lavington (ed.). Information Processing. Vol. 80. North-Holland, Amsterdam. pp. 613–619. arXiv:1004.3621.