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authorMichaŽl Baudin <michael.baudin@scilab.org>2009-02-17 12:05:16 +0100
committerMichaŽl Baudin <michael.baudin@scilab.org>2009-02-17 12:05:16 +0100
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Update for references of complex division
Diffstat (limited to 'scilab_doc')
-rw-r--r--scilab_doc/scilabisnotnaive/complexdivision.tex17
-rw-r--r--scilab_doc/scilabisnotnaive/scilabisnotnaive.bib38
-rw-r--r--scilab_doc/scilabisnotnaive/scilabisnotnaive.pdfbin294439 -> 299187 bytes
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diff --git a/scilab_doc/scilabisnotnaive/complexdivision.tex b/scilab_doc/scilabisnotnaive/complexdivision.tex
index a38738f..e09ab56 100644
--- a/scilab_doc/scilabisnotnaive/complexdivision.tex
+++ b/scilab_doc/scilabisnotnaive/complexdivision.tex
@@ -520,4 +520,21 @@ Stewart's algorithm is superseded by the one by Li et Al \cite{567808}, but
520also by Kahan's \cite{KAHAN1987}, which, from \cite{1039814}, is the one implemented 520also by Kahan's \cite{KAHAN1987}, which, from \cite{1039814}, is the one implemented
521in the C99 standard. 521in the C99 standard.
522 522
523\subsection{References}
524
525The 1962 paper by R. Smith \cite{368661} describes the algorithm which is used in
526Scilab. The Goldberg paper \cite{WhatEveryComputerScientist} introduces many
527of the subjects presented in this document, including the problem of the
528complex division. The 1985 paper by Stewart \cite{214414} gives insight to
529distinguish between the relative error of the complex numbers and the relative
530error made on real and imaginary parts. It also gives an algorithm based
531on min and max functions. Knuth's bible \cite{artcomputerKnuthVol2} presents
532the Smith's method in section 4.2.1, as exercize 16. Knuth gives also
533references \cite{Wynn:1962:AAP} and \cite{DBLP:journals/cacm/Friedland67}.
534The 1967 paper by Friedland \cite{DBLP:journals/cacm/Friedland67} describes
535two algorithm to compute the absolute value of a complex number
536$|x+iy| = \sqrt{x^2+y^2}$ and the square root of a
537complex number $\sqrt{x+iy}$.
538
539
523 540
diff --git a/scilab_doc/scilabisnotnaive/scilabisnotnaive.bib b/scilab_doc/scilabisnotnaive/scilabisnotnaive.bib
index 28d3776..6de801c 100644
--- a/scilab_doc/scilabisnotnaive/scilabisnotnaive.bib
+++ b/scilab_doc/scilabisnotnaive/scilabisnotnaive.bib
@@ -203,3 +203,41 @@ pages={75-87},
203doi={10.1109/C-M.1981.220382}, 203doi={10.1109/C-M.1981.220382},
204ISSN={0018-9162}, } 204ISSN={0018-9162}, }
205 205
206@book{artcomputerKnuthVol2,
207author = {D. E. Knuth},
208title = {The Art of Computer Programming, Volume 2, Seminumerical Algorithms},
209year = {1998},
210publisher= {Third Edition, Addison Wesley, Reading, MA}}
211
212@Article{Wynn:1962:AAP,
213 author = "P. Wynn",
214 title = "An Arsenal of {ALGOL} Procedures for Complex
215 Arithmetic",
216 journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
217 volume = "2",
218 number = "4",
219 pages = "232--255",
220 month = dec,
221 year = "1962",
222 CODEN = "BITTEL, NBITAB",
223 DOI = "http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/BF01940171",
224 ISSN = "0006-3835 (print), 1572-9125 (electronic)",
225 bibdate = "Wed Jan 4 18:52:07 MST 2006",
226 bibsource = "ftp://ftp.math.utah.edu/pub/tex/bib/bit.bib;
227 http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=2&issue=4",
228 URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=2&issue=4&spage=232",
229 acknowledgement = ack-nhfb,
230}
231@article{DBLP:journals/cacm/Friedland67,
232 author = {Paul Friedland},
233 title = {Algorithm 312: Absolute value and square root of a complex
234 number},
235 journal = {Commun. ACM},
236 volume = {10},
237 number = {10},
238 year = {1967},
239 pages = {665},
240 ee = {http://doi.acm.org/10.1145/363717.363780},
241 bibsource = {DBLP, http://dblp.uni-trier.de}
242}
243
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