Class information for:
Level 1: MATRIX POLYNOMIAL//POLYNOMIAL EIGENVALUE PROBLEM//STABILITY RADIUS

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
8229 1278 20.5 41%


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
943 2             LINEAR ALGEBRA AND ITS APPLICATIONS//SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS//MOORE PENROSE INVERSE 10922
8229 1                   MATRIX POLYNOMIAL//POLYNOMIAL EIGENVALUE PROBLEM//STABILITY RADIUS 1278

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 MATRIX POLYNOMIAL authKW 727252 6% 39% 79
2 POLYNOMIAL EIGENVALUE PROBLEM authKW 500035 2% 70% 30
3 STABILITY RADIUS authKW 495580 4% 45% 46
4 HAMILTONIAN MATRIX authKW 441955 3% 50% 37
5 QUADRATIC EIGENVALUE PROBLEM authKW 398144 3% 42% 40
6 PSEUDOSPECTRA authKW 373011 3% 43% 36
7 PSEUDOSPECTRUM authKW 367456 3% 42% 37
8 BACKWARD ERROR authKW 325146 3% 39% 35
9 COMPANION FORM authKW 305804 1% 80% 16
10 SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS journal 294070 13% 8% 162

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 40352 70% 0% 891
2 Mathematics 14723 46% 0% 594
3 Automation & Control Systems 2770 10% 0% 127
4 Computer Science, Software Engineering 222 4% 0% 45
5 Operations Research & Management Science 137 3% 0% 36
6 Computer Science, Theory & Methods 33 2% 0% 27
7 Mathematics, Interdisciplinary Applications 33 2% 0% 21
8 Engineering, General 16 1% 0% 18
9 Engineering, Electrical & Electronic 14 5% 0% 62
10 Mechanics 11 2% 0% 27

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 DIPARTIMENTO INGN SCI INFORMAT MATEMAT 106420 1% 64% 7
2 MA 4 5 99546 0% 83% 5
3 VIETNAM UNIV HCMC 99546 0% 83% 5
4 MATH MA 4 5 90046 1% 54% 7
5 AFDELING WISKUNDE 82132 1% 25% 14
6 EXACTE WETEN PEN 74216 1% 18% 17
7 AG NUMER 66361 0% 56% 5
8 CU MI VOIX 63708 0% 67% 4
9 FAK MATH MATH IND TECH 53754 0% 75% 3
10 UNIT BMI 52714 1% 28% 8

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 SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 294070 13% 8% 162
2 LINEAR ALGEBRA AND ITS APPLICATIONS 233845 26% 3% 335
3 ELECTRONIC JOURNAL OF LINEAR ALGEBRA 67639 3% 6% 44
4 ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS 12123 1% 3% 17
5 NUMERISCHE MATHEMATIK 8677 3% 1% 33
6 BIT NUMERICAL MATHEMATICS 7728 2% 1% 22
7 NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 7599 1% 2% 18
8 SYSTEMS & CONTROL LETTERS 6383 3% 1% 33
9 OPERATORS AND MATRICES 6090 1% 2% 11
10 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE 5250 1% 1% 16

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 MATRIX POLYNOMIAL 727252 6% 39% 79 Search MATRIX+POLYNOMIAL Search MATRIX+POLYNOMIAL
2 POLYNOMIAL EIGENVALUE PROBLEM 500035 2% 70% 30 Search POLYNOMIAL+EIGENVALUE+PROBLEM Search POLYNOMIAL+EIGENVALUE+PROBLEM
3 STABILITY RADIUS 495580 4% 45% 46 Search STABILITY+RADIUS Search STABILITY+RADIUS
4 HAMILTONIAN MATRIX 441955 3% 50% 37 Search HAMILTONIAN+MATRIX Search HAMILTONIAN+MATRIX
5 QUADRATIC EIGENVALUE PROBLEM 398144 3% 42% 40 Search QUADRATIC+EIGENVALUE+PROBLEM Search QUADRATIC+EIGENVALUE+PROBLEM
6 PSEUDOSPECTRA 373011 3% 43% 36 Search PSEUDOSPECTRA Search PSEUDOSPECTRA
7 PSEUDOSPECTRUM 367456 3% 42% 37 Search PSEUDOSPECTRUM Search PSEUDOSPECTRUM
8 BACKWARD ERROR 325146 3% 39% 35 Search BACKWARD+ERROR Search BACKWARD+ERROR
9 COMPANION FORM 305804 1% 80% 16 Search COMPANION+FORM Search COMPANION+FORM
10 SKEW HAMILTONIAN MATRIX 286697 1% 100% 12 Search SKEW+HAMILTONIAN+MATRIX Search SKEW+HAMILTONIAN+MATRIX

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 DE TERAN, F , DOPICO, FM , MACKEY, DS , (2014) SPECTRAL EQUIVALENCE OF MATRIX POLYNOMIALS AND THE INDEX SUM THEOREM.LINEAR ALGEBRA AND ITS APPLICATIONS. VOL. 459. ISSUE . P. 264 -333 31 89% 8
2 AHMAD, SS , MEHRMANN, V , (2016) BACKWARD ERRORS AND PSEUDOSPECTRA FOR STRUCTURED NONLINEAR EIGENVALUE PROBLEMS.OPERATORS AND MATRICES. VOL. 10. ISSUE 3. P. 539 -556 28 88% 0
3 MACKEY, DS , MACKEY, N , MEHL, C , MEHRMANN, V , (2013) SKEW-SYMMETRIC MATRIX POLYNOMIALS AND THEIR SMITH FORMS.LINEAR ALGEBRA AND ITS APPLICATIONS. VOL. 438. ISSUE 12. P. 4625 -4653 25 96% 6
4 DMYTRYSHYN, A , FUTORNY, V , KAGSTROM, B , KLIMENKO, L , SERGEICHUK, VV , (2015) CHANGE OF THE CONGRUENCE CANONICAL FORM OF 2-BY-2 AND 3-BY-3 MATRICES UNDER PERTURBATIONS AND BUNDLES OF MATRICES UNDER CONGRUENCE.LINEAR ALGEBRA AND ITS APPLICATIONS. VOL. 469. ISSUE . P. 305 -334 24 96% 0
5 MEHL, C , MEHRMANN, V , RAN, ACM , RODMAN, L , (2016) EIGENVALUE PERTURBATION THEORY OF STRUCTURED REAL MATRICES AND THEIR SIGN CHARACTERISTICS UNDER GENERIC STRUCTURED RANK-ONE PERTURBATIONS.LINEAR & MULTILINEAR ALGEBRA. VOL. 64. ISSUE 3. P. 527 -556 23 96% 0
6 BUENO, MI , DOPICO, FM , FURTADO, S , RYCHNOVSKY, M , (2015) LARGE VECTOR SPACES OF BLOCK-SYMMETRIC STRONG LINEARIZATIONS OF MATRIX POLYNOMIALS.LINEAR ALGEBRA AND ITS APPLICATIONS. VOL. 477. ISSUE . P. 165 -210 21 100% 1
7 KAROW, M , (2011) STRUCTURED PSEUDOSPECTRA FOR SMALL PERTURBATIONS.SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS. VOL. 32. ISSUE 4. P. 1383-1398 25 86% 2
8 RODMAN, L , (2014) INVARIANT NEUTRAL SUBSPACES FOR HAMILTONIAN MATRICES.ELECTRONIC JOURNAL OF LINEAR ALGEBRA. VOL. 27. ISSUE . P. 55-99 22 92% 0
9 ADHIKARI, B , ALAM, R , KRESSNER, D , (2011) STRUCTURED EIGENVALUE CONDITION NUMBERS AND LINEARIZATIONS FOR MATRIX POLYNOMIALS.LINEAR ALGEBRA AND ITS APPLICATIONS. VOL. 435. ISSUE 9. P. 2193-2221 22 96% 2
10 KAROW, M , MENGI, E , (2015) MATRIX POLYNOMIALS WITH SPECIFIED EIGENVALUES.LINEAR ALGEBRA AND ITS APPLICATIONS. VOL. 466. ISSUE . P. 457 -482 19 100% 0

Classes with closest relation at Level 1


Rank Class id link
1 14267 NONLINEAR MATRIX EQUATION//NONSYMMETRIC ALGEBRAIC RICCATI EQUATION//POSITIVE DEFINITE SOLUTION
2 8262 SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS//NUMERICAL RANK//RANK REVEALING
3 22041 CONTROLLABILITY INDICES//MATEMAT LICADA EIO//BRUNOVSKY INDICES
4 23472 FINITE HORIZON LQ PROBLEM//DISCRETE TIME ALGEBRAIC RICCATI EQUATION//UNMIXED SOLUTIONS
5 24535 SEMISEPARABLE MATRICES//QUASISEPARABLE MATRICES//QR ITERATION
6 22726 PARTIALLY PRESCRIBED SPECTRAL INFORMATION//PARTIALLY PRESCRIBED SPECTRAL DATA//INVERSE QUADRATIC EIGENVALUE PROBLEM
7 26152 COXETER FUNCTOR//BELITSKIIS ALGORITHM//INDECOMPOSABLE SYSTEM
8 4176 GMRES//MULTIPLE RIGHT HAND SIDES//NONSYMMETRIC LINEAR SYSTEMS
9 28890 FBI BARGMANN TRANSFORM//COMPLEX PERTURBATION//INFINITE CURVATURE
10 25628 MULTIPARAMETER EIGENVALUE PROBLEM//TWO PARAMETER//NONLINEAR STURM LIOUVILLE

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