Class information for:
Level 1: ILL POSED PROBLEM//DISCREPANCY PRINCIPLE//TIKHONOV REGULARIZATION

Basic class information
Class id #P Avg. number of
references		 Database coverage
of references
7830 1322 22.2 46%


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
16 4 ENGINEERING, CIVIL//CONSTRUCTION & BUILDING TECHNOLOGY//MECHANICS 627508
437 3       ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS//ELECTRICAL IMPEDANCE TOMOGRAPHY//INVERSE PROBLEMS 26987
1985 2             ILL POSED PROBLEM//INVERSE HEAT CONDUCTION PROBLEM//DISCREPANCY PRINCIPLE 5570
7830 1                   ILL POSED PROBLEM//DISCREPANCY PRINCIPLE//TIKHONOV REGULARIZATION 1322

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 ILL POSED PROBLEM authKW 1169153 16% 24% 213
2 DISCREPANCY PRINCIPLE authKW 938875 5% 57% 71
3 TIKHONOV REGULARIZATION authKW 733730 12% 21% 155
4 NONLINEAR ILL POSED PROBLEMS authKW 561788 2% 81% 30
5 DISCRETE ILL POSED PROBLEMS authKW 443438 2% 80% 24
6 JOURNAL OF INVERSE AND ILL-POSED PROBLEMS journal 417481 6% 22% 83
7 INVERSE PROBLEMS journal 386554 18% 7% 239
8 REGULARIZATION authKW 346956 17% 7% 227
9 LINEAR ILL POSED PROBLEMS authKW 266281 1% 82% 14
10 HILBERT SCALES authKW 259825 1% 75% 15

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 55843 80% 0% 1063
2 Physics, Mathematical 7848 22% 0% 289
3 Mathematics 2635 20% 0% 269
4 Computer Science, Software Engineering 337 4% 0% 55
5 Mathematics, Interdisciplinary Applications 211 3% 0% 44
6 Engineering, General 143 3% 0% 40
7 Operations Research & Management Science 57 2% 0% 26
8 Mechanics 32 3% 0% 37
9 COMPUTER APPLICATIONS & CYBERNETICS 31 0% 0% 2
10 Computer Science, Theory & Methods 31 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 IND MATH 225464 5% 16% 61
2 JOHANN RADON COMPUTAT PL MATH 66145 2% 10% 30
3 BASIC TEACHING MINIST 46192 0% 100% 2
4 IND MATH HBEREICH 3 46192 0% 100% 2
5 HBEREICH 03 38487 0% 33% 5
6 MATH CIRAM 36949 0% 40% 4
7 GEOMATH SICHUAN 34641 0% 50% 3
8 STAT INVERSE PROBLEMS BIOPHYS GRP 34641 0% 50% 3
9 ZENTRUM TECHNOMATH 34216 1% 11% 13
10 CEFET BA 30794 0% 67% 2

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 INVERSE AND ILL-POSED PROBLEMS 417481 6% 22% 83
2 INVERSE PROBLEMS 386554 18% 7% 239
3 JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS 28843 1% 8% 15
4 NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 28394 4% 3% 48
5 ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS 23376 2% 4% 24
6 INVERSE PROBLEMS AND IMAGING 19576 2% 4% 20
7 BIT NUMERICAL MATHEMATICS 17877 3% 2% 34
8 NUMERISCHE MATHEMATIK 14938 3% 1% 44
9 NUMERICAL ALGORITHMS 11606 2% 2% 30
10 APPLICABLE ANALYSIS 11456 2% 2% 27

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 ILL POSED PROBLEM 1169153 16% 24% 213 Search ILL+POSED+PROBLEM Search ILL+POSED+PROBLEM
2 DISCREPANCY PRINCIPLE 938875 5% 57% 71 Search DISCREPANCY+PRINCIPLE Search DISCREPANCY+PRINCIPLE
3 TIKHONOV REGULARIZATION 733730 12% 21% 155 Search TIKHONOV+REGULARIZATION Search TIKHONOV+REGULARIZATION
4 NONLINEAR ILL POSED PROBLEMS 561788 2% 81% 30 Search NONLINEAR+ILL+POSED+PROBLEMS Search NONLINEAR+ILL+POSED+PROBLEMS
5 DISCRETE ILL POSED PROBLEMS 443438 2% 80% 24 Search DISCRETE+ILL+POSED+PROBLEMS Search DISCRETE+ILL+POSED+PROBLEMS
6 REGULARIZATION 346956 17% 7% 227 Search REGULARIZATION Search REGULARIZATION
7 LINEAR ILL POSED PROBLEMS 266281 1% 82% 14 Search LINEAR+ILL+POSED+PROBLEMS Search LINEAR+ILL+POSED+PROBLEMS
8 HILBERT SCALES 259825 1% 75% 15 Search HILBERT+SCALES Search HILBERT+SCALES
9 SOURCE CONDITION 230152 1% 59% 17 Search SOURCE+CONDITION Search SOURCE+CONDITION
10 GENERAL SOURCE CONDITIONS 214969 1% 85% 11 Search GENERAL+SOURCE+CONDITIONS Search GENERAL+SOURCE+CONDITIONS

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 GAZZOLA, S , NOVATI, P , RUSSO, MR , (2015) ON KRYLOV PROJECTION METHODS AND TIKHONOV REGULARIZATION.ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS. VOL. 44. ISSUE . P. 83 -123 44 90% 7
2 REICHEL, L , RODRIGUEZ, G , (2013) OLD AND NEW PARAMETER CHOICE RULES FOR DISCRETE ILL-POSED PROBLEMS.NUMERICAL ALGORITHMS. VOL. 63. ISSUE 1. P. 65-87 29 91% 26
3 BAUER, F , LUKAS, MA , (2011) COMPARING PARAMETER CHOICE METHODS FOR REGULARIZATION OF ILL-POSED PROBLEMS.MATHEMATICS AND COMPUTERS IN SIMULATION. VOL. 81. ISSUE 9. P. 1795 -1841 46 49% 64
4 LANDI, G , PICCOLOMINI, EL , TOMBA, I , (2016) A STOPPING CRITERION FOR ITERATIVE REGULARIZATION METHODS.APPLIED NUMERICAL MATHEMATICS. VOL. 106. ISSUE . P. 53 -68 29 83% 0
5 WERNER, F , (2015) ON CONVERGENCE RATES FOR ITERATIVELY REGULARIZED NEWTON-TYPE METHODS UNDER A LIPSCHITZ-TYPE NONLINEARITY CONDITION.JOURNAL OF INVERSE AND ILL-POSED PROBLEMS. VOL. 23. ISSUE 1. P. 75 -84 26 90% 2
6 CHEN, DH , HOFMANN, B , ZOU, J , (2017) ELASTIC-NET REGULARIZATION VERSUS L(1)-REGULARIZATION FOR LINEAR INVERSE PROBLEMS WITH QUASI-SPARSE SOLUTIONS.INVERSE PROBLEMS. VOL. 33. ISSUE 1. P. - 25 86% 0
7 FLEMMING, J , (2013) VARIATIONAL SMOOTHNESS ASSUMPTIONS IN CONVERGENCE RATE THEORY-AN OVERVIEW.JOURNAL OF INVERSE AND ILL-POSED PROBLEMS. VOL. 21. ISSUE 3. P. 395-409 23 100% 1
8 HOFMANN, B , MATHE, P , (2012) PARAMETER CHOICE IN BANACH SPACE REGULARIZATION UNDER VARIATIONAL INEQUALITIES.INVERSE PROBLEMS. VOL. 28. ISSUE 10. P. - 22 100% 11
9 PORNSAWAD, P , BOCKMANN, C , (2016) MODIFIED ITERATIVE RUNGE-KUTTA-TYPE METHODS FOR NONLINEAR ILL-POSED PROBLEMS.NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION. VOL. 37. ISSUE 12. P. 1562 -1589 20 100% 0
10 HAMARIK, U , PALM, R , RAUS, T , (2010) EXTRAPOLATION OF TIKHONOV REGULARIZATION METHOD.MATHEMATICAL MODELLING AND ANALYSIS. VOL. 15. ISSUE 1. P. 55-68 22 100% 9

Classes with closest relation at Level 1


Rank Class id link
1 29071 DYNAMICAL SYSTEMS METHOD DSM//INTEGRO INTERPOLATION//NUMERICAL DIFFERENTIATION
2 18640 WAVELET MULTISCALE METHOD//INVERSE COEFFICIENT PROBLEM//COEFFICIENT IDENTIFICATION
3 13310 DATA COMPLETION//CAUCHY PROBLEM//ROBIN INVERSE PROBLEM
4 2836 TOTAL VARIATION//IMAGE RESTORATION//IMAGE DENOISING
5 35642 IMPLICIT LINEAR OPERATORS//MATRIX DIAGONAL EXTRACTION//TRACE ESTIMATION
6 7697 ILL POSED PROBLEM//INVERSE SOURCE PROBLEM//BACKWARD HEAT PROBLEM
7 11163 WHITE NOISE MODEL//ADAPTIVE ESTIMATION//MINIMAX RISK
8 21213 SMOOTHING SPLINES//GENERALIZED CROSS VALIDATION//SMOOTHING PARAMETER
9 28552 WEEKS METHOD//SLOWLY CONVERGENT SERIES//LAPLACE TRANSFORM INVERSION
10 6532 BLIND DECONVOLUTION//IMAGE RESTORATION//IMAGE DEBLURRING

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