Class information for:
Level 1: NUMERICAL ALGEBRAIC GEOMETRY//POLYNOMIAL SYSTEMS//HOMOTOPY CONTINUATION

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
17322 606 22.0 36%


Bar chart of Publication_year

Last years might be incomplete

Hierarchy of classes
The table includes all classes above and classes immediately below the current class.


Cluster id Level Cluster label #P
15 4 MATHEMATICS//MATHEMATICS, APPLIED//MATH 719832
485 3       LINEAR ALGEBRA AND ITS APPLICATIONS//BENFORDS LAW//MATHEMATICS, APPLIED 23484
2135 2             ORDER OF CONVERGENCE//SEMILOCAL CONVERGENCE//NONLINEAR EQUATIONS 5069
17322 1                   NUMERICAL ALGEBRAIC GEOMETRY//POLYNOMIAL SYSTEMS//HOMOTOPY CONTINUATION 606

Terms with highest relevance score


rank Term termType Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 NUMERICAL ALGEBRAIC GEOMETRY authKW 1008771 5% 65% 31
2 POLYNOMIAL SYSTEMS authKW 791009 10% 26% 61
3 HOMOTOPY CONTINUATION authKW 466565 4% 36% 26
4 POLYHEDRAL HOMOTOPY authKW 458063 2% 91% 10
5 C 1 HOMOTOPY authKW 453484 1% 100% 9
6 COMPONENTS OF SOLUTIONS authKW 453484 1% 100% 9
7 MULTIPLICITY STRUCTURE authKW 352710 1% 100% 7
8 APPROXIMATE GCD authKW 274327 1% 78% 7
9 REGULAR VALUE authKW 274327 1% 78% 7
10 WITNESS SET authKW 259132 1% 86% 6

Web of Science journal categories


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 Mathematics, Applied 15404 63% 0% 380
2 Computer Science, Theory & Methods 2152 17% 0% 102
3 Mathematics 2093 26% 0% 159
4 Computer Science, Software Engineering 302 6% 0% 34
5 Automation & Control Systems 120 3% 0% 20
6 Physics, Mathematical 40 3% 0% 18
7 Operations Research & Management Science 27 2% 0% 12
8 Computer Science, Interdisciplinary Applications 11 2% 0% 11
9 Mathematics, Interdisciplinary Applications 8 1% 0% 8
10 Computer Science, Information Systems 6 1% 0% 9

Address terms


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 PL COMPUTAT MATH STAT 64756 2% 9% 15
2 CARAMEL PROJECT 50387 0% 100% 1
3 COMPLEX SYST DESIGN 50387 0% 100% 1
4 FRE 2656CNRS 50387 0% 100% 1
5 INFORMAT TELECOMS 50387 0% 100% 1
6 INSA ENERGET SYST PRO 50387 0% 100% 1
7 KU LEUVEN IMINDS 50387 0% 100% 1
8 LAS CHENGDU 50387 0% 100% 1
9 LESPINSA ROUEN 50387 0% 100% 1
10 P COMPUTAT MATH STAT 50387 0% 100% 1

Journals


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class
1 JOURNAL OF SYMBOLIC COMPUTATION 16258 4% 1% 27
2 SIAM JOURNAL ON NUMERICAL ANALYSIS 12573 5% 1% 32
3 APPLIED MATHEMATICS AND COMPUTATION 9311 9% 0% 57
4 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE 7328 2% 1% 13
5 FOUNDATIONS OF COMPUTATIONAL MATHEMATICS 6269 1% 2% 7
6 NUMERISCHE MATHEMATIK 4859 3% 1% 17
7 MATHEMATICS OF COMPUTATION 4556 3% 0% 19
8 EXPERIMENTAL MATHEMATICS 4426 1% 1% 8
9 DISCRETE & COMPUTATIONAL GEOMETRY 2941 2% 1% 11
10 JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2834 4% 0% 24

Author Key Words


Rank Term Chi square Shr. of publ. in
class containing
term		 Class's shr. of
term's tot. occurrences		 #P with
term in
class		 LCSH search Wikipedia search
1 NUMERICAL ALGEBRAIC GEOMETRY 1008771 5% 65% 31 Search NUMERICAL+ALGEBRAIC+GEOMETRY Search NUMERICAL+ALGEBRAIC+GEOMETRY
2 POLYNOMIAL SYSTEMS 791009 10% 26% 61 Search POLYNOMIAL+SYSTEMS Search POLYNOMIAL+SYSTEMS
3 HOMOTOPY CONTINUATION 466565 4% 36% 26 Search HOMOTOPY+CONTINUATION Search HOMOTOPY+CONTINUATION
4 POLYHEDRAL HOMOTOPY 458063 2% 91% 10 Search POLYHEDRAL+HOMOTOPY Search POLYHEDRAL+HOMOTOPY
5 C 1 HOMOTOPY 453484 1% 100% 9 Search C+1+HOMOTOPY Search C+1+HOMOTOPY
6 COMPONENTS OF SOLUTIONS 453484 1% 100% 9 Search COMPONENTS+OF+SOLUTIONS Search COMPONENTS+OF+SOLUTIONS
7 MULTIPLICITY STRUCTURE 352710 1% 100% 7 Search MULTIPLICITY+STRUCTURE Search MULTIPLICITY+STRUCTURE
8 APPROXIMATE GCD 274327 1% 78% 7 Search APPROXIMATE+GCD Search APPROXIMATE+GCD
9 REGULAR VALUE 274327 1% 78% 7 Search REGULAR+VALUE Search REGULAR+VALUE
10 WITNESS SET 259132 1% 86% 6 Search WITNESS+SET Search WITNESS+SET

Core articles
The table includes core articles in the class. The following variables is taken into account for the relevance score of an article in a cluster c:
(1) Number of references referring to publications in the class.
(2) Share of total number of active references referring to publications in the class.
(3) Age of the article. New articles get higher score than old articles.
(4) Citation rate, normalized to year.


Rank Reference # ref.
in cl.		 Shr. of ref. in
cl.		 Citations
1 CHEN, TR , LEE, TL , LI, TY , (2017) MIXED CELL COMPUTATION IN HOM4PS-3.JOURNAL OF SYMBOLIC COMPUTATION. VOL. 79. ISSUE . P. 516 -534 27 77% 1
2 HAUENSTEIN, JD , WAMPLER, CW , (2017) UNIFICATION AND EXTENSION OF INTERSECTION ALGORITHMS IN NUMERICAL ALGEBRAIC GEOMETRY.APPLIED MATHEMATICS AND COMPUTATION. VOL. 293. ISSUE . P. 226 -243 28 88% 0
3 VERSCHELDE, J , (1999) ALGORITHM 795: PHCPACK: A GENERAL-PURPOSE SOLVER FOR POLYNOMIAL SYSTEMS BY HOMOTOPY CONTINUATION.ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE. VOL. 25. ISSUE 2. P. 251-276 40 70% 223
4 SU, HJ , MCCARTHY, JM , SOSONKINA, M , WATSON, LT , (2006) ALGORITHM 857: POLSYS_GLP - A PARALLEL GENERAL LINEAR PRODUCT HOMOTOPY CODE FOR SOLVING POLYNOMIAL SYSTEMS OF EQUATIONS.ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE. VOL. 32. ISSUE 4. P. 561 -579 27 96% 10
5 LEE, TL , LI, TY , TSAI, CH , (2008) HOM4PS-2.0: A SOFTWARE PACKAGE FOR SOLVING POLYNOMIAL SYSTEMS BY THE POLYHEDRAL HOMOTOPY CONTINUATION METHOD.COMPUTING. VOL. 83. ISSUE 2-3. P. 109 -133 21 91% 75
6 WINKLER, JR , YANG, N , (2013) RESULTANT MATRICES AND THE COMPUTATION OF THE DEGREE OF AN APPROXIMATE GREATEST COMMON DIVISOR OF TWO INEXACT BERNSTEIN BASIS POLYNOMIALS.COMPUTER AIDED GEOMETRIC DESIGN. VOL. 30. ISSUE 4. P. 410-429 21 91% 1
7 JIAO, LB , DONG, B , ZHANG, JT , YU, B , (2016) POLYNOMIAL HOMOTOPY METHOD FOR THE SPARSE INTERPOLATION PROBLEM PART I: EQUALLY SPACED SAMPLING.SIAM JOURNAL ON NUMERICAL ANALYSIS. VOL. 54. ISSUE 1. P. 462 -480 23 77% 0
8 YU, B , DONG, B , (2008) A HYBRID POLYNOMIAL SYSTEM SOLVING METHOD FOR MIXED TRIGONOMETRIC POLYNOMIAL SYSTEMS.SIAM JOURNAL ON NUMERICAL ANALYSIS. VOL. 46. ISSUE 3. P. 1503 -1518 21 91% 1
9 DONG, B , YU, B , YU, Y , (2014) A SYMMETRIC HOMOTOPY AND HYBRID POLYNOMIAL SYSTEM SOLVING METHOD FOR MIXED TRIGONOMETRIC POLYNOMIAL SYSTEMS.MATHEMATICS OF COMPUTATION. VOL. 83. ISSUE 288. P. 1847-1868 18 90% 1
10 LEYKIN, A , VERSCHELDE, J , ZHUANG, Y , (2006) PARALLEL HOMOTOPY ALGORITHMS TO SOLVE POLYNOMIAL SYSTEMS.MATHEMATICAL SOFTWARE-ICMS 2006, PROCEEDINGS. VOL. 4151. ISSUE . P. 225 -234 19 95% 1

Classes with closest relation at Level 1


Rank Class id link
1 17049 IMPLICITLY DEFINED CURVE//BIALTERNATE PRODUCT//UNILATERAL DYNAMIC CONTACT
2 6132 JOURNAL OF SYMBOLIC COMPUTATION//POLYNOMIAL SYSTEM SOLVING//MATEMAT ESTADIST COMPUTAC
3 16500 SIMULTANEOUS METHODS//POLYNOMIAL ZEROS//INCLUSION METHODS
4 21638 IDEAL PROJECTOR//KERGIN INTERPOLATION//RADON PROJECTIONS
5 9792 MECHANISM AND MACHINE THEORY//ARMAMENTS ENGN TECHNOL//MOTION GENERATION
6 12943 EIGENSTRUCTURE ASSIGNMENT//POLE PLACEMENT//POLE ASSIGNMENT
7 5398 COMPUTER AIDED GEOMETRIC DESIGN//PYTHAGOREAN HODOGRAPH CURVES//DEGREE REDUCTION
8 19307 SIMPLICIAL ALGORITHM//INTEGER LABELING//SPLITTING OPERATION
9 21759 LITTLEWOOD RICHARDSON COEFFICIENTS//KRONECKER COEFFICIENTS//GEOMETRIC COMPLEXITY THEORY
10 15613 INTERVAL LINEAR SYSTEM//INTERVAL LINEAR EQUATIONS//AE SOLUTION SETS

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