Class information for:
Level 1: NUMERICAL VERIFICATION//SPECTRAL POLLUTION//NUMERICAL VERIFICATION METHOD

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
25007 294 17.1 33%


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
25007 1                   NUMERICAL VERIFICATION//SPECTRAL POLLUTION//NUMERICAL VERIFICATION METHOD 294

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 VERIFICATION authKW 1549348 11% 45% 33
2 SPECTRAL POLLUTION authKW 1402119 6% 75% 18
3 NUMERICAL VERIFICATION METHOD authKW 738568 3% 89% 8
4 INTERPOLATION ERROR CONSTANTS authKW 311584 1% 100% 3
5 NUMERICAL APPROXIMATION OF THE SPECTRUM authKW 311584 1% 100% 3
6 SECOND ORDER SPECTRUM authKW 311584 1% 100% 3
7 VERIFIED COMPUTATION authKW 302132 3% 36% 8
8 COMPUTER ASSISTED PROOF authKW 236684 5% 16% 14
9 KOLMOGOROV FLOWS authKW 233687 1% 75% 3
10 BABUSKA AZIZ CONSTANT authKW 207723 1% 100% 2

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 9849 72% 0% 211
2 Mathematics 1345 30% 0% 88
3 Mechanics 263 11% 0% 33
4 Computer Science, Theory & Methods 103 6% 0% 17
5 Computer Science, Software Engineering 20 2% 0% 7
6 Mathematics, Interdisciplinary Applications 14 2% 0% 6
7 Computer Science, Hardware & Architecture 10 1% 0% 4
8 Physics, Mathematical 7 2% 0% 6
9 Computer Science, Information Systems 2 1% 0% 4
10 Multidisciplinary Sciences 2 1% 0% 2

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 ECOLE PONTS PARISTECH INRIA 207723 1% 100% 2
2 BERUFSAKAD THURINGEN 103861 0% 100% 1
3 STATE UNIV LVOV POLYTECHN 103861 0% 100% 1
4 ANGEW NUMER MATH 1 51930 0% 50% 1
5 WALES MATH COMPUTAT SCI 23077 1% 11% 2
6 ANAL TECH MATH VERSICHERUNGSMATH 20771 0% 20% 1
7 PROJET MICMAC 20771 0% 20% 1
8 MATH 1 18656 3% 2% 8
9 INFANT EDUC 17309 0% 17% 1
10 NWF 1 MATH 17309 0% 17% 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 JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 50444 5% 3% 15
2 ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK 16786 10% 1% 28
3 JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 11852 12% 0% 34
4 JOURNAL OF SPECTRAL THEORY 10925 1% 3% 4
5 COMPUTING 9514 4% 1% 13
6 IMA JOURNAL OF NUMERICAL ANALYSIS 7168 3% 1% 10
7 NUMERISCHE MATHEMATIK 6812 5% 0% 14
8 NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 4486 3% 0% 9
9 SIAM JOURNAL ON NUMERICAL ANALYSIS 2524 3% 0% 10
10 INTEGRAL EQUATIONS AND OPERATOR THEORY 2267 2% 0% 7

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 VERIFICATION 1549348 11% 45% 33 Search NUMERICAL+VERIFICATION Search NUMERICAL+VERIFICATION
2 SPECTRAL POLLUTION 1402119 6% 75% 18 Search SPECTRAL+POLLUTION Search SPECTRAL+POLLUTION
3 NUMERICAL VERIFICATION METHOD 738568 3% 89% 8 Search NUMERICAL+VERIFICATION+METHOD Search NUMERICAL+VERIFICATION+METHOD
4 INTERPOLATION ERROR CONSTANTS 311584 1% 100% 3 Search INTERPOLATION+ERROR+CONSTANTS Search INTERPOLATION+ERROR+CONSTANTS
5 NUMERICAL APPROXIMATION OF THE SPECTRUM 311584 1% 100% 3 Search NUMERICAL+APPROXIMATION+OF+THE+SPECTRUM Search NUMERICAL+APPROXIMATION+OF+THE+SPECTRUM
6 SECOND ORDER SPECTRUM 311584 1% 100% 3 Search SECOND+ORDER+SPECTRUM Search SECOND+ORDER+SPECTRUM
7 VERIFIED COMPUTATION 302132 3% 36% 8 Search VERIFIED+COMPUTATION Search VERIFIED+COMPUTATION
8 COMPUTER ASSISTED PROOF 236684 5% 16% 14 Search COMPUTER+ASSISTED+PROOF Search COMPUTER+ASSISTED+PROOF
9 KOLMOGOROV FLOWS 233687 1% 75% 3 Search KOLMOGOROV+FLOWS Search KOLMOGOROV+FLOWS
10 BABUSKA AZIZ CONSTANT 207723 1% 100% 2 Search BABUSKA+AZIZ+CONSTANT Search BABUSKA+AZIZ+CONSTANT

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 NAKAO, MT , (2001) NUMERICAL VERIFICATION METHODS FOR SOLUTIONS OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS.NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION. VOL. 22. ISSUE 3-4. P. 321 -356 28 97% 25
2 WATANABE, Y , NAGATOU, K , PLUM, M , NAKAO, MT , (2016) NORM BOUND COMPUTATION FOR INVERSES OF LINEAR OPERATORS IN HILBERT SPACES.JOURNAL OF DIFFERENTIAL EQUATIONS. VOL. 260. ISSUE 7. P. 6363 -6374 18 100% 0
3 HINCHCLIFFE, J , STRAUSS, M , (2016) SPECTRAL ENCLOSURE AND SUPERCONVERGENCE FOR EIGENVALUES IN GAPS.INTEGRAL EQUATIONS AND OPERATOR THEORY. VOL. 84. ISSUE 1. P. 1 -32 20 87% 0
4 BOULTON, L , (2016) SPECTRAL POLLUTION AND EIGENVALUE BOUNDS.APPLIED NUMERICAL MATHEMATICS. VOL. 99. ISSUE . P. 1 -23 17 81% 2
5 WATANABE, Y , NAKAO, MT , (2016) A NUMERICAL VERIFICATION METHOD FOR NONLINEAR FUNCTIONAL EQUATIONS BASED ON INFINITE-DIMENSIONAL NEWTON-LIKE ITERATION.APPLIED MATHEMATICS AND COMPUTATION. VOL. 276. ISSUE . P. 239 -251 15 94% 0
6 STRAUSS, M , (2014) A NEW APPROACH TO SPECTRAL APPROXIMATION.JOURNAL OF FUNCTIONAL ANALYSIS. VOL. 267. ISSUE 8. P. 3084 -3103 17 81% 3
7 WATANABE, Y , NAGATOU, K , PLUM, M , NAKAO, MT , (2014) VERIFIED COMPUTATIONS OF EIGENVALUE EXCLOSURES FOR EIGENVALUE PROBLEMS IN HILBERT SPACES.SIAM JOURNAL ON NUMERICAL ANALYSIS. VOL. 52. ISSUE 2. P. 975-992 13 93% 1
8 NAKAO, MT , WATANABE, Y , KINOSHITA, T , KIMURA, T , YAMAMOTO, N , (2015) SOME CONSIDERATIONS OF THE INVERTIBILITY VERIFICATIONS FOR LINEAR ELLIPTIC OPERATORS.JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS. VOL. 32. ISSUE 1. P. 19 -31 11 100% 0
9 BOULTON, L , STRAUSS, M , (2011) ON THE CONVERGENCE OF SECOND-ORDER SPECTRA AND MULTIPLICITY.PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES. VOL. 467. ISSUE 2125. P. 264 -284 11 100% 1
10 SHARGORODSKY, E , (2013) ON THE LIMIT BEHAVIOUR OF SECOND ORDER RELATIVE SPECTRA OF SELF-ADJOINT OPERATORS.JOURNAL OF SPECTRAL THEORY. VOL. 3. ISSUE 4. P. 535 -552 11 92% 2

Classes with closest relation at Level 1


Rank Class id link
1 21592 ERROR FREE TRANSFORMATION//FLOATING POINT ARITHMETIC//FLOATING POINT SUMMATION
2 25276 CP METHODS//STURM LIOUVILLE PROBLEM//ASYMPTOTIC CORRECTION
3 14916 CONLEY INDEX//RIGOROUS NUMERICS//COMPUTER ASSISTED PROOF
4 28890 FBI BARGMANN TRANSFORM//COMPLEX PERTURBATION//INFINITE CURVATURE
5 15613 INTERVAL LINEAR SYSTEM//INTERVAL LINEAR EQUATIONS//AE SOLUTION SETS
6 30295 CUICBAS//ARBITRARY BOUNDARIES//INHOMOGENEOUS STRING
7 17049 IMPLICITLY DEFINED CURVE//BIALTERNATE PRODUCT//UNILATERAL DYNAMIC CONTACT
8 6366 A POSTERIORI ERROR ESTIMATES//NONCONFORMING FINITE ELEMENT//A POSTERIORI ERROR ESTIMATOR
9 28229 ABC MATH PROGRAM//SPECTRAL SUBSPACE//ISOSPECTRAL GRAPH REDUCTION
10 8229 MATRIX POLYNOMIAL//POLYNOMIAL EIGENVALUE PROBLEM//STABILITY RADIUS

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