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Publication numberUST915008 I4
Publication typeGrant
Publication dateOct 9, 1973
Filing dateApr 6, 1973
Priority dateApr 6, 1973
Publication numberUS T915008 I4, US T915008I4, US-I4-T915008, UST915008 I4, UST915008I4
InventorsF. G. Gustavson
Export CitationBiBTeX, EndNote, RefMan
External Links: USPTO, USPTO Assignment, Espacenet
Yes yes
US T915008 I4
Abstract  available in
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Description  (OCR text may contain errors)

DEFENSIVE PUBLICATION UNITED STATES PATENT OFFICE Published at the request of the applicant or owner in accordance with the Notice of Dec. 16. 1969, 869 O.G. 687. The abstracts of Defensive Publication applications are identified by distinctly numbered series and are arranged chronologically. The heading of each abstract indicates the number of pages of specification, including claims and sheets of drawings contained in the application as originally filed. The files of these applications are available to the public for inspection and reproduction may be purchased for 30 cents a sheet.

Defensive Publication applications have not been examined as to the merits of alleged invention. The Patent Oflice makes no assertion as to the novelty of the disclosed subject matter.

PUBLISHED OCTOBER 9, 1973 10 METHOD FOR EFFECTING GAUSS ELIMINATION X IN SPARSE MATRIX TECHNIQUES Fred G. Gustavson and Gary D. Hachtel, Ossining, N.Y.,

assignors to International Business Machines Corpora- PERFORM ORDEMNG 12 tion Armonk N.Y. FiledApr. 1973, Ser. No 348,833 BASED ON WEIGHTED OPERATION COUNT Int. Cl. G06f 7/38 US. Cl. 444-1 3 Sheets a 32 Pages Specification OOMPUTE VA=V(G(A)) AND DA-D(O(A)) H4 A novel method is disclosed for solving the equation 1 A[t,x]y=e =col (0,0, ,0,1) for various values of t, and, for each I, for many distinct values of x, and wherei i in, there is combined the storage advantages of the looping, pro-indexed fill technique with the inherent speed S'Q J QKjg'i i and storage advantages of the 1-2-3 GNSO technique for obtaining a minimum storage, medium speed algorithm for solving the above equation. The method defines a new type of decomposition of the Gauss elimination matrix, G(A) of a given matrix A(x,t) into partial Gauss elimination of distinct matrices T(t) and X(x,t), wherein T contains the necessary and sufiicient data structure for t-type operations in G(A), i.e., T contains only non- START oop BY v u mc zero elements which are used in wholly t-type operations X(x,t)-(VA-2)*A+(DA-2)*G (T,A) in G(A), and X contains the necessary and sufficient data structure for the x-type operations. In addition, the method defines algorithms for the two distinct partial Gauss eliminations G (T,A) and G (X,A), employing a looping pro-indexed, variability typed fill technique. The method eliminates the necessity for precompiling, i.e., generating and storing instructions for type-decomposed Gauss elimination of the 1-2-3 GNSO approach, and extends irnmediately to the case of three or more distinct variability types appearing as arguments in the coeflicients of the matrix A.

Oct. 9, 1973 F. G. GUSTAVSQN ET L T915303 METHOD FOR EFFECTING GAUSS ELIMINATION IN SPARSE MATRIX TECHNIQUES Filed April 6, 1975 3 Sheets-Sheet l FIG.1

INITIALIZE x AND L -10 PERFORM ORDERING BASED ON WEIGHTED OPERATION COUNT OOMPUTE VA=V(G(A)) AND DA=D(G(A)) 14 START t-LOOP BY EVALUATING T(t)=(V(A)=1)-*A CALCULATE GT=G1(T,A) 18 START X-LOOP BY EVALUATING X(X,)=(VA=2)*A+(DA-2)*G1(T,A)

CALCULATE GX= G2(X,A) 22 LAST X FOR THIS I 24 YES NO IF LAST t,STOP UPDATE x UPDATE t 28

Referenced by
Citing PatentFiling datePublication dateApplicantTitle
US5157778 *Apr 23, 1990Oct 20, 1992Digital Equipment CorporationMethod and apparatus for circuit simulation using parallel processors including memory arrangements and matrix decomposition synchronization
WO1988001412A1 *Aug 20, 1987Feb 25, 1988Digital Equipment CorpMethod and apparatus for circuit simulation using parallel processors including memory arrangement and matrix decomposition synchronization
Classifications
U.S. Classification708/446
International ClassificationG06F17/11, G06F17/12, G06F17/16
Cooperative ClassificationG06F17/16, G06F17/12
European ClassificationG06F17/12, G06F17/16