Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Remark on algorithm 16: crout with pivoting

Remark on algorithm 16: crout with pivoting REMARK ON ALGORITHM 16 CROUT W1Ttt PIVOTING (G. F o r s y t h e , Communications A C M , S e p t e m b e r , 1960) GEORGE E. FORSYTHE Stanford University, Stanford, Californi~ QUERY Perhaps the most basic procedure for an AL(I()L library of matrix programs is an inner product procedure. The pro-cedure Innerproduct given on page 311 of [1] is f:drly difficult to comprehend, and probably poses great difficulties for most translating routines. I merely copied its form in writing a modified inner product routine for [2]. My query is: How should one write an inner product procedure in ALGOL? REFERENCES 1. PE'rZR N~UR (editor), J. W. BACKUS, ET AL., Report on the algorithmic language ALGOL 60, Comtn. Assoc. Com.p. Mach. 8 (1960), 299-314. 2. GEOaGE E. FORSYTHE, CROUT with pivoting in ALGOL 60, Comm. Assoc. Cutup. Mach. 8 (1960), 507-508. A/gerihms E, ALGORiTHX[ 20 REAL EXPONENTIAL INTEGI{AL S. P:~.~w N a t i o n a l B t t r e t m of S t a n d a r d s , W ~ s h i n g t o n real p r o c e d u r e colnlnellt 25, D.C. Expire (x) ; real x ; - - E i ( - x ) = f~ (e "/tL) du is conq)uted for x > 0 [)3' approximation i'ormulas. For 0 < x < 1 the approxim:~tion is from E. E. Allen, Note 169, MTAC 56, pg 240 (1954). Illt The second approximation formula is for series I < x < ~ and is from C. flastings, ,Jr., ~w0 "Approximations l?or Digital Computers" e0ral!: (Princeton University Press, Princeton, stleh New Jersey, 1955). The absolute error e(x) is le(x)l < 2 X 10-7 for 0 < x < 1 f011r and Ie(x){ < 2 X l()-s for I < x < ~¢ ; shiffi realy, w, z ; begin ALGORITHM 19 BINOMIAL COEFFICIENTS RI(~ARI) R . KENYOX~ Computing Laboratory, Purdue Indiana comment if x < [ t h e n z := (((( .00107857 X x - - .00976004) X x + .005519968) N: x--..24991055) X x + .99999193) X x -~ .57721566 - - In(x) else begin University, Lafayette, This procedure computes binomial coefficients Cm~ = n!/m!(n - - m)! by the recursion formula Ci%1 = (n - - 1)Ci~/(i 47 1) starting from Co~ = 1 ; procedure C ( m , n) ; m, n ; i n t e g e r i, a, b y := ((( x + 8.5733287401) X x + 18.059016973) X x + 8.6347608925) X x 49 + .2677737343 ; w := ((( x + 9.5733223454) )4 x + 25.6329561486) X x + 21.0996530827) X x 47 3.95849692~8 z := exp l - - x ) / x X ( y / w ) e n d Expint := z e n d integer integer begin ( ; a:=l ; i f 2 X m > n t h e n b := n - - m e l s e b:=m ; f o r i := 0 s t e p 1 u n t i l b d o b e g i n a : = (n - - i) X a + end (i 47 1) e n d Standards Corrigenda* C:=a Binomial Coefficients Contributions to this department must be in the form stated in the Algorithms D e p a r t m e n t policy statement (Communications, February, 1960) except that ALGOL 60 notation should be used (see Communications, May, 1960). Contributions should be sent to J. H. Wegstein, Computation Laboratory, National Bureau of Standards, Washing. ton 25, D.C. Algorithms should be in the Publication form of ALGOL 60 and written in a style patterned after the most recent algorithras appearing in this department. Although each algorithm has been tested by its contributor, no warranty, express or implied, is made by the contributor, the editor, or the Association for Computing Machinery as to the accuracy and functioning of the algorithm and related algorithm material and no responsibility is assumed by the contributor, the editor, or the Association for Computing Machinery in connection therewith, ............................................................................................................... j EDWARD A. VOORI-IEES, " S o m e T h o u g h t s o n Reconciling V a r i o u s C h a r a c t e r S e t P r o p o s a"l s , " Comm. A C M 3 (July 1960), 4 0 8 - 9 : 11 T i l e c h a r a c t e r set (:hart is r e p r o d u c e d (p. 541) wifl~ the c o r r e c t i o n of t w o c h a r a c t e r s in t h e 1 2 0 - C h a r a c t e r Se~. T h e t w o c o r r e c t e d c h a r a c t e r s a p p e a r i n tile; t h i r d line, ) f o m ' t h f r o m t h e e n d , c o r r e c t l y : D ; a n d i n t h e fifth li~e, t h e t h i r d f r o m tile b e g i m f i n g , c o r r e c t l y : ~ . * T h e s e e r r o r s wo e introd,,,.,,d ,n t h e p r o d u c t i o n th0 issue ; apologies are extended to both the author and the Staudards i Editor. Communications of the ACM http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications of the ACM Association for Computing Machinery

Remark on algorithm 16: crout with pivoting

Forsythe, George E.
Communications of the ACM , Volume 3 (10) – Oct 1, 1960
Download PDF
1 page

Loading next page...
 
/lp/association-for-computing-machinery/remark-on-algorithm-16-crout-with-pivoting-eeCSpycpa1

References (2)

Publisher
Association for Computing Machinery
Copyright
Copyright © 1960 by ACM Inc.
ISSN
0001-0782
DOI
10.1145/367415.367428
Publisher site
See Article on Publisher Site

Abstract

REMARK ON ALGORITHM 16 CROUT W1Ttt PIVOTING (G. F o r s y t h e , Communications A C M , S e p t e m b e r , 1960) GEORGE E. FORSYTHE Stanford University, Stanford, Californi~ QUERY Perhaps the most basic procedure for an AL(I()L library of matrix programs is an inner product procedure. The pro-cedure Innerproduct given on page 311 of [1] is f:drly difficult to comprehend, and probably poses great difficulties for most translating routines. I merely copied its form in writing a modified inner product routine for [2]. My query is: How should one write an inner product procedure in ALGOL? REFERENCES 1. PE'rZR N~UR (editor), J. W. BACKUS, ET AL., Report on the algorithmic language ALGOL 60, Comtn. Assoc. Com.p. Mach. 8 (1960), 299-314. 2. GEOaGE E. FORSYTHE, CROUT with pivoting in ALGOL 60, Comm. Assoc. Cutup. Mach. 8 (1960), 507-508. A/gerihms E, ALGORiTHX[ 20 REAL EXPONENTIAL INTEGI{AL S. P:~.~w N a t i o n a l B t t r e t m of S t a n d a r d s , W ~ s h i n g t o n real p r o c e d u r e colnlnellt 25, D.C. Expire (x) ; real x ; - - E i ( - x ) = f~ (e "/tL) du is conq)uted for x > 0 [)3' approximation i'ormulas. For 0 < x < 1 the approxim:~tion is from E. E. Allen, Note 169, MTAC 56, pg 240 (1954). Illt The second approximation formula is for series I < x < ~ and is from C. flastings, ,Jr., ~w0 "Approximations l?or Digital Computers" e0ral!: (Princeton University Press, Princeton, stleh New Jersey, 1955). The absolute error e(x) is le(x)l < 2 X 10-7 for 0 < x < 1 f011r and Ie(x){ < 2 X l()-s for I < x < ~¢ ; shiffi realy, w, z ; begin ALGORITHM 19 BINOMIAL COEFFICIENTS RI(~ARI) R . KENYOX~ Computing Laboratory, Purdue Indiana comment if x < [ t h e n z := (((( .00107857 X x - - .00976004) X x + .005519968) N: x--..24991055) X x + .99999193) X x -~ .57721566 - - In(x) else begin University, Lafayette, This procedure computes binomial coefficients Cm~ = n!/m!(n - - m)! by the recursion formula Ci%1 = (n - - 1)Ci~/(i 47 1) starting from Co~ = 1 ; procedure C ( m , n) ; m, n ; i n t e g e r i, a, b y := ((( x + 8.5733287401) X x + 18.059016973) X x + 8.6347608925) X x 49 + .2677737343 ; w := ((( x + 9.5733223454) )4 x + 25.6329561486) X x + 21.0996530827) X x 47 3.95849692~8 z := exp l - - x ) / x X ( y / w ) e n d Expint := z e n d integer integer begin ( ; a:=l ; i f 2 X m > n t h e n b := n - - m e l s e b:=m ; f o r i := 0 s t e p 1 u n t i l b d o b e g i n a : = (n - - i) X a + end (i 47 1) e n d Standards Corrigenda* C:=a Binomial Coefficients Contributions to this department must be in the form stated in the Algorithms D e p a r t m e n t policy statement (Communications, February, 1960) except that ALGOL 60 notation should be used (see Communications, May, 1960). Contributions should be sent to J. H. Wegstein, Computation Laboratory, National Bureau of Standards, Washing. ton 25, D.C. Algorithms should be in the Publication form of ALGOL 60 and written in a style patterned after the most recent algorithras appearing in this department. Although each algorithm has been tested by its contributor, no warranty, express or implied, is made by the contributor, the editor, or the Association for Computing Machinery as to the accuracy and functioning of the algorithm and related algorithm material and no responsibility is assumed by the contributor, the editor, or the Association for Computing Machinery in connection therewith, ............................................................................................................... j EDWARD A. VOORI-IEES, " S o m e T h o u g h t s o n Reconciling V a r i o u s C h a r a c t e r S e t P r o p o s a"l s , " Comm. A C M 3 (July 1960), 4 0 8 - 9 : 11 T i l e c h a r a c t e r set (:hart is r e p r o d u c e d (p. 541) wifl~ the c o r r e c t i o n of t w o c h a r a c t e r s in t h e 1 2 0 - C h a r a c t e r Se~. T h e t w o c o r r e c t e d c h a r a c t e r s a p p e a r i n tile; t h i r d line, ) f o m ' t h f r o m t h e e n d , c o r r e c t l y : D ; a n d i n t h e fifth li~e, t h e t h i r d f r o m tile b e g i m f i n g , c o r r e c t l y : ~ . * T h e s e e r r o r s wo e introd,,,.,,d ,n t h e p r o d u c t i o n th0 issue ; apologies are extended to both the author and the Staudards i Editor. Communications of the ACM

Journal

Communications of the ACM – Association for Computing Machinery

Published: Oct 1, 1960

There are no references for this article.