An Algorithm for Solving the Absolute Value Equation

0329208 - ÚI 2010 RIV IL eng J - Článek v odborném periodiku
Rohn, Jiří
An Algorithm for Solving the Absolute Value Equation.
[Algoritmus pro řešení rovnice s absolutní hodnotou.]
Electronic Journal of Linear Algebra. Roč. 18, - (2009), s. 589-599. ISSN 1537-9582. E-ISSN 1081-3810
Grant CEP: GA ČR GA201/09/1957; GA ČR GC201/08/J020
Výzkumný záměr: CEZ:AV0Z10300504
Klíčová slova: absolute value equation * algorithm * regularity * singularity * theorem of the alternatives
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.892, rok: 2009
http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol18_pp589-599.pdf

Citováno: 36

--- WANG, A.X. - WANG, H.J. - DENG, Y.K. Interval algorithm for absolute value equations. CENTRAL EUROPEAN JOURNAL OF MATHEMATICS. ISSN 1895-1074, OCT 2011, vol. 9, no. 5, p. 1171-1184. [WOS]
--- YONG, L.Q. Social Cognitive Optimization for Absolute Value Equations. 2010 ETP/IITA CONFERENCE ON SYSTEM SCIENCE AND SIMULATION IN ENGINEERING (SSSE 2010). 2010, p. 161-164. [WOS]
--- YONG, L.Q. Differential Evolution Algorithm for Absolute Value Equations. 2010 ETP/IITA CONFERENCE ON TELECOMMUNICATION AND INFORMATION (TEIN 2010). 2010, p. 52-55. [WOS]
--- LI, W. - WANG, H.P. - WANG, Q. Localized solutions to interval linear equations. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. ISSN 0377-0427, JAN 15 2012, vol. 238, p. 29-38. [WOS]
--- LI, C.X. A Preconditioned AOR Iterative Method for the Absolute Value Equations. INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS. ISSN 0219-8762, MAR 2017, vol. 14, no. 2. [WOS]
--- LI, C.X. On the modified Hermitian and skew-Hermitian splitting iteration methods for a class of weakly absolute value equations. JOURNAL OF INEQUALITIES AND APPLICATIONS. ISSN 1029-242X, OCT 21 2016. [WOS]
--- LI, C.X. A Modified Generalized Newton Method for Absolute Value Equations. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. ISSN 0022-3239, SEP 2016, vol. 170, no. 3, p. 1055-1059. [WOS]
--- WU, S.L. - GUO, P. On the Unique Solvability of the Absolute Value Equation. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. ISSN 0022-3239, MAY 2016, vol. 169, no. 2, p. 705-712. [WOS]
--- LI, C.X. - WU, S.L. A note on the unique solution of linear complementarity problem. COGENT MATHEMATICS. ISSN 2331-1835, 2016, vol. 3. [WOS]
--- YONG, L.Q. Smooth Newton method to absolute value equation based on lower uniform smoothing approximation function. JOURNAL OF INTERDISCIPLINARY MATHEMATICS. ISSN 0972-0502, 2016, vol. 19, no. 1, p. 191-205. [WOS]
--- ESMAEILI, H. - MAHMOODABADI, E. - AHMADI, M. A UNIFORM APPROXIMATION METHOD TO SOLVE ABSOLUTE VALUE EQUATION. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY. ISSN 1735-8515, OCT-NOV 2015, vol. 41, no. 5, p. 1259-1269. [WOS]
--- MOOSAEI, H. - KETABCHI, S. - NOOR, M.A. - IQBAL, J. - HOOSHYARBAKHSH, V. Some techniques for solving absolute value equations. APPLIED MATHEMATICS AND COMPUTATION. ISSN 0096-3003, OCT 1 2015, vol. 268, p. 696-705. [WOS]
--- MANGASARIAN, O.L. A hybrid algorithm for solving the absolute value equation. OPTIMIZATION LETTERS. ISSN 1862-4472, OCT 2015, vol. 9, no. 7, p. 1469-1474. [WOS]
--- GRIEWANK, A. - BERNT, J.U. - RADONS, M. - STREUBEL, T. Solving piecewise linear systems in abs-normal form. LINEAR ALGEBRA AND ITS APPLICATIONS. ISSN 0024-3795, APR 15 2015, vol. 471, p. 500-530. [WOS]
--- YONG, L.Q. Iteration Method for Absolute Value Equation and Applications in Two-point Boundary Value Problem of Linear Differential Equation. JOURNAL OF INTERDISCIPLINARY MATHEMATICS. ISSN 0972-0502, 2015, vol. 18, no. 4, p. 355-374. [WOS]
--- YONG, L.Q. Improved Harmony Search Algorithm based on Cluster for Absolute Value Equation with 2(n) Solutions. 2015 27TH CHINESE CONTROL AND DECISION CONFERENCE (CCDC). ISSN 1948-9439, 2015, p. 3770-3775. [WOS]
--- YONG, L.Q. Improved Harmony Search Algorithm with Differential Operator for Absolute Value Equation. 2015 27TH CHINESE CONTROL AND DECISION CONFERENCE (CCDC). ISSN 1948-9439, 2015, p. 3786-3790. [WOS]
--- MANGASARIAN, O.L. Absolute Value Equation Solution Via Linear Programming. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. ISSN 0022-3239, JUN 2014, vol. 161, no. 3, p. 870-876. [WOS]
--- JIANG, X.Q. - ZHANG, Y. A SMOOTHING-TYPE ALGORITHM FOR ABSOLUTE VALUE EQUATIONS. JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION. ISSN 1547-5816, OCT 2013, vol. 9, no. 4, p. 789-798. [WOS]
--- MANGASARIAN, O.L. Absolute value equation solution via dual complementarity. OPTIMIZATION LETTERS. ISSN 1862-4472, APR 2013, vol. 7, no. 4, p. 625-630. [WOS]
--- WANG, H.J. - LIU, H. - CAO, S.Y. A verification method for enclosing solutions of absolute value equations. COLLECTANEA MATHEMATICA. ISSN 0010-0757, JAN 2013, vol. 64, no. 1, p. 17-38. [WOS]
--- MANGASARIAN, O.L. Primal-dual bilinear programming solution of the absolute value equation. OPTIMIZATION LETTERS. ISSN 1862-4472, OCT 2012, vol. 6, no. 7, SI, p. 1527-1533. [WOS]
--- YONG, L.Q. Potential Reduction Interior Point Algorithm for Absolute Value Equations. 2011 30TH CHINESE CONTROL CONFERENCE (CCC). ISSN 2161-2927, 2011, p. 2072-2075. [WOS]
--- YONG, L.Q. A Survey of Recent Development in Absolute Value Equations. PROCEEDINGS OF THE FOURTH INTERNATIONAL CONFERENCE OF MODELLING AND SIMULATION (ICMS2011), VOL 1. 2011, p. 284-287. [WOS]
--- WANG, A. - CAO, Y. - CHEN, J.X. Modified Newton-Type Iteration Methods for Generalized Absolute Value Equations. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. ISSN 0022-3239, APR 2019, vol. 181, no. 1, p. 216-230. [WOS]
--- LI, Y. - DU, S.Q. Modified HS conjugate gradient method for solving generalized absolute value equations. JOURNAL OF INEQUALITIES AND APPLICATIONS. ISSN 1029-242X, MAR 19 2019. [WOS]
--- NGUYEN, C.T. - SAHEYA, B. - CHANG, Y.L. - CHEN, J.S. Unified smoothing functions for absolute value equation associated with second-order cone. APPLIED NUMERICAL MATHEMATICS. ISSN 0168-9274, JAN 2019, vol. 135, p. 206-227. [WOS]
--- YAMANAKA, S. - YAMASHITA, N. Duality of nonconvex optimization with positively homogeneous functions. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. ISSN 0926-6003, NOV 2018, vol. 71, no. 2, p. 435-456. [WOS]
--- MANSOORI, A. - ERFANIAN, M. A dynamic model to solve the absolute value equations. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. ISSN 0377-0427, MAY 1 2018, vol. 333, p. 28-35. [WOS]
--- ROHN, J. - SHARY, S.P. Interval matrices: Regularity generates singularity. LINEAR ALGEBRA AND ITS APPLICATIONS. ISSN 0024-3795, MAR 1 2018, vol. 540, p. 149-159. [WOS]
--- HE, J. - LIU, Y.M. - TIAN, J.K. Two numerical iteration methods for solving absolute value equations. SCIENCEASIA. ISSN 1513-1874, FEB 2018, vol. 44, no. 1, p. 40-45. [WOS]
--- SAHEYA, B. - YU, C.H. - CHEN, J.S. Numerical comparisons based on four smoothing functions for absolute value equation. JOURNAL OF APPLIED MATHEMATICS AND COMPUTING. ISSN 1598-5865, FEB 2018, vol. 56, no. 1-2, p. 131-149. [WOS]
--- WU, S.L. - LI, C.X. The unique solution of the absolute value equations. APPLIED MATHEMATICS LETTERS. ISSN 0893-9659, FEB 2018, vol. 76, p. 195-200. [WOS]
--- ABDALLAH, L. - HADDOU, M. - MIGOT, T. Solving absolute value equation using complementarity and smoothing functions. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. ISSN 0377-0427, JAN 1 2018, vol. 327, p. 196-207. [WOS]
--- MIAO, X.H. - YANG, J.T. - SAHEYA, B. - CHEN, J.S. A smoothing Newton method for absolute value equation associated with second-order cone. APPLIED NUMERICAL MATHEMATICS. ISSN 0168-9274, OCT 2017, vol. 120, p. 82-96. [WOS]
--- LVA, C.Q. - MA, C.F. Picard splitting method and Picard CG method for solving the absolute value equation. JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS. ISSN 2008-1898, 2017, vol. 10, no. 7, p. 3643-3654. [WOS]

Trvalý link: http://hdl.handle.net/11104/0175306