http://rdf.ncbi.nlm.nih.gov/pubchem/patent/US-T915007-I4
Outgoing Links
| Predicate | Object |
|---|---|
| classificationCPCInventive | http://rdf.ncbi.nlm.nih.gov/pubchem/patentcpc/G06F17-13 http://rdf.ncbi.nlm.nih.gov/pubchem/patentcpc/G06F17-16 |
| classificationIPCInventive | http://rdf.ncbi.nlm.nih.gov/pubchem/patentipc/G06F17-16 http://rdf.ncbi.nlm.nih.gov/pubchem/patentipc/G06F17-13 |
| filingDate | 1973-04-05-04:00^^<http://www.w3.org/2001/XMLSchema#date> |
| grantDate | 1973-10-09-04:00^^<http://www.w3.org/2001/XMLSchema#date> |
| publicationDate | 1973-10-09-04:00^^<http://www.w3.org/2001/XMLSchema#date> |
| publicationNumber | US-T915007-I4 |
| titleOfInvention | Call tsolv |
| abstract | A METHOD IS DESCRIBED WHICH INCORPORATES SPARSE MATRIX TECHNIQUES FOR EFFICIENTLY EFFECTING THE BACK SUBSTITUTION STEP IN THE SOLVING OF THE LINEAR SYSTEM FOR VARIOUS VALUES OF T, AND FOR EACH T, FOR VARIOUS VALUES OF X, THE SOLVING OF SUCH LINEAR SYSTEM USUALLY BEING NECESSARY IN THE SOLVING OF NON-LINEAR DYNAMIC SYSTEMS. THE REQUIRED STEPS IN THE SOLVING OF THE LINEAR SYSTEM ARE L/U (LOWER, UPPER) TRIANGULAR FACTORIZATION, FOWARD ELIMINATION AND THE ABOVE-MENTIONED BACK SUBSTITUTION. EQUATION 1 MAY BE RESTATED AS A(X,T)Y=EN=COL (0, 0, ..., 1) WHERE AND UTILIZING 1-2-3 GNSO TECHNIQUE, THE SOLVING OF EQUATIONS 2A AND 2B IMPLIES THE SUCCESSIVE OPERATIONS OF FACTORIZATION LA/UA=A(X,T) AND BACK SUBSTITUTION UAY=EN THE INVENTIVE METHOD OVERCOME THE PROBLEM WHICH ARISES IN THE SOLUTION OF EQUATION 4 IN THAT THERE ARE REQUIRED AS OUTPUTS FOR EACH VALUE OF X AND T ONLY PARTIAL ANSWERS YX=$X*(UX-1EN)=$X*$X SELECTION OF PIVOTS, (3) IT CONVERTS ALGORITHMS FOR MINIMIZING L/U FACTORIZATION OF MATRICES WITH X AND T VARIABILITY TYPE INTO ALGORITHMS WHICH MINIMIZE MULTIPLES FOR THE COMBINED OPERATIONS OF FACTORIZATION AND PARTIAL BACK SUBSTITUTION, I.E., IT ACHIEVES STEPS (1)-(3), (4) IT ACHIEVES STEPS (1)-(3) IN THE CASE OF MORE THAN TWO DISTINCT VARIABILITY TYPES, (5) IT APPLIES AS WRITTEN TO CASES WHERE A IS IRREDUCBLE BUT ACHIEVES STEPS (1)-(3) WITH REDUCIBLE MATRICES AND THE CORRESPONDING PARTIAL BACK SUBSTITUTION MATRICES UX AND UT, (2) IT MAKES IDENTIFICATION (1) SOLELY FROM THE PROCESS OF GAUSS ELIMINATION WHEREBY THE OPERATION COUNT FOR THE PARTIAL BACK SUBSTITUTION IS ACCOUNTED FOR DURING THE $X AND $T ONCE FOR EACH T, WHERE UX AND UT ARE SUBMATRICES OF UA. THE INVENTIVE METHOD PERFORMS THE FOLLOWING FUNCTIONS: (1) IT IDENTIFIES THE "SPARSEST" PARTIAL OUTPUT VECTORS YT=$T*(UT-1YX)=$T*$T ONCE FOR EACH X, AND WHEREIN $X AND $T ARE LOGICAL VECTORS AND "*" REPRESENTS SCALAR MULTIPLICATION. THE PARTIAL ANSWERS FOR THE PROBLEM IN BACK SUBSTITUTION IS THE ASCERTAINING OF THE SPARSEST MATRICES UX AND UT FROM WHICH THERE MAY E OBTAINED YX AND YT UTILIZING THE PARTIAL BACK SUBSTITUTIONS YT=$T*Y AND YX=$X*Y |
| priorityDate | 1973-04-05-04:00^^<http://www.w3.org/2001/XMLSchema#date> |
| type | http://data.epo.org/linked-data/def/patent/Publication |
Incoming Links
| Predicate | Subject |
|---|---|
| isDiscussedBy | http://rdf.ncbi.nlm.nih.gov/pubchem/compound/CID104858 http://rdf.ncbi.nlm.nih.gov/pubchem/substance/SID419569864 |
Total number of triples: 14.