0105250 - UIVT-O 20040241 RIV GB eng J - Journal Article
Rohn, Jiří
A Theorem of the Alternatives for the Equation Ax + B|x| = b.
[Věta o alternativách pro rovnici Ax+B|x|=b.]
Linear & Multilinear Algebra. Roč. 52, č. 6 (2004), s. 421-426. ISSN 0308-1087. E-ISSN 1563-5139
R&D Projects: GA ČR GA201/01/0343
Institutional research plan: CEZ:AV0Z1030915
Keywords : nonlinear equation * existence * uniqueness * interval matrix * eigenvalue
Subject RIV: BA - General Mathematics
Impact factor: 0.377, year: 2004
DOI: https://doi.org/10.1080/0308108042000220686

Cited: 67

--- MANGASARIAN, O.L. Absolute value programming. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. ISSN 0926-6003, JAN 2007, vol. 36, no. 1, p. 43-53. [WOS]
--- PROKOPYEV, O. On equivalent reformulations for absolute value equations. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. ISSN 0926-6003, DEC 2009, vol. 44, no. 3, p. 363-372. [WOS]
--- ZHANG, C. - WEI, Q.J. Global and Finite Convergence of a Generalized Newton Method for Absolute Value Equations. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. ISSN 0022-3239, NOV 2009, vol. 143, no. 2, p. 391-403. [WOS]
--- MANGASARIAN, O.L. Absolute value equation solution via concave minimization. OPTIMIZATION LETTERS. ISSN 1862-4472, JAN 2007, vol. 1, no. 1, p. 3-8. [WOS]
--- MANGASARIAN, O.L. A generalized Newton method for absolute value equations. OPTIMIZATION LETTERS. ISSN 1862-4472, JAN 2009, vol. 3, no. 1, p. 101-108. [WOS]
--- 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]
--- MANGASARIAN, O.L. - RECHT, B. Probability of unique integer solution to a system of linear equations. EUROPEAN JOURNAL OF OPERATIONAL RESEARCH. ISSN 0377-2217, OCT 1 2011, vol. 214, no. 1, p. 27-30. [WOS]
--- KARADEMIR, S. - PROKOPYEV, O.A. A short note on solvability of systems of interval linear equations. LINEAR & MULTILINEAR ALGEBRA. ISSN 0308-1087, 2011, vol. 59, no. 6, p. 707-710. [WOS]
--- CACCETTA, L. - QU, B.A. - ZHOU, G.L. A globally and quadratically convergent method for absolute value equations. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. ISSN 0926-6003, JAN 2011, vol. 48, no. 1, p. 45-58. [WOS]
--- HU, S.L. - HUANG, Z.H. - ZHANG, Q.O. A generalized Newton method for absolute value equations associated with second order cones. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. ISSN 0377-0427, JAN 1 2011, vol. 235, no. 5, p. 1490-1501. [WOS]
--- HU, S.L. - HUANG, Z.H. A note on absolute value equations. OPTIMIZATION LETTERS. ISSN 1862-4472, AUG 2010, vol. 4, no. 3, p. 417-424. [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]
--- NOOR, M.A. - IQBAL, J. - NOOR, K.I. - AL-SAID, E. Generalized AOR Method for Solving Absolute Complementarity Problems. JOURNAL OF APPLIED MATHEMATICS. ISSN 1110-757X, 2012. [WOS]
--- NOOR, M.A. - IQBAL, J. - AL-SAID, E. Residual Iterative Method for Solving Absolute Value Equations. ABSTRACT AND APPLIED ANALYSIS. ISSN 1085-3375, 2012. [WOS]
--- NOOR, M.A. - IQBAL, J. - NOOR, K.I. - AL-SAID, E. On an iterative method for solving absolute value equations. OPTIMIZATION LETTERS. ISSN 1862-4472, JUN 2012, vol. 6, no. 5, p. 1027-1033. [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]
--- 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]
--- 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]
--- 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]
--- MIAO, X.H. - YANG, J.T. - HU, S.L. A generalized Newton method for absolute value equations associated with circular cones. APPLIED MATHEMATICS AND COMPUTATION. ISSN 0096-3003, OCT 15 2015, vol. 269, p. 155-168. [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]
--- ZHANG, J.J. The relaxed nonlinear PHSS-like iteration method for absolute value equations. APPLIED MATHEMATICS AND COMPUTATION. ISSN 0096-3003, AUG 15 2015, vol. 265, p. 266-274. [WOS]
--- HAGHANI, F.K. On Generalized Traub's Method for Absolute Value Equations. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. ISSN 0022-3239, AUG 2015, vol. 166, no. 2, p. 619-625. [WOS]
--- IQBAL, J. - IQBAL, A. - ARIF, M. Levenberg-Marquardt method for solving systems of absolute value equations. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. ISSN 0377-0427, JUL 2015, vol. 282, p. 134-138. [WOS]
--- GAJARDO, P. - SEEGER, A. Equilibrium problems involving the Lorentz cone. JOURNAL OF GLOBAL OPTIMIZATION. ISSN 0925-5001, FEB 2014, vol. 58, no. 2, p. 321-340. [WOS]
--- YAMANAKA, S. - FUKUSHIMA, M. A branch-and-bound method for absolute value programs. OPTIMIZATION. ISSN 0233-1934, FEB 1 2014, vol. 63, no. 2, p. 305-319. [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]
--- NOOR, M.A. - NOOR, K.I. - IQBAL, J. Generalized symmetric accelerated over relaxation method for solving absolute value complementarity problems. COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS. ISSN 0965-5425, MAR 2013, vol. 53, no. 3, p. 265-272. [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]
--- KE, Y.F. - MA, C.F. SOR-like iteration method for solving absolute value equations. APPLIED MATHEMATICS AND COMPUTATION. ISSN 0096-3003, OCT 15 2017, vol. 311, p. 195-202. [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]
--- EDALATPOUR, V. - HEZARI, D. - SALKUYEH, D.K. A generalization of the Gauss-Seidel iteration method for solving absolute value equations. APPLIED MATHEMATICS AND COMPUTATION. ISSN 0096-3003, JAN 15 2017, vol. 293, p. 156-167. [WOS]
--- YONG, L.Q. - TUO, S.H. - SHI, J.R. Sparse solution of some special optimization problems. JOURNAL OF INTERDISCIPLINARY MATHEMATICS. ISSN 0972-0502, 2017, vol. 20, no. 2, p. 595-602. [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]
--- CRUZ, J.Y.B. - FERREIRA, O.P. - PRUDENTE, L.F. On the global convergence of the inexact semi-smooth Newton method for absolute value equation. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. ISSN 0926-6003, SEP 2016, vol. 65, no. 1, p. 93-108. [WOS]
--- FENG, J.M. - LIU, S.Y. An improved generalized Newton method for absolute value equations. SPRINGERPLUS. ISSN 2193-1801, JUL 11 2016, vol. 5. [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]
--- JING, L. - FEI, Q. - JIE, L. - BIN, Z. A New Iterative Method for Solving Absolute Value Equations. PROCEEDINGS OF 2016 12TH INTERNATIONAL CONFERENCE ON COMPUTATIONAL INTELLIGENCE AND SECURITY (CIS). 2016, p. 555-556. [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. - MIRZAPOUR, M. - MAHMOODABADI, E. A FAST CONVERGENT TWO-STEP ITERATIVE METHOD TO SOLVE THE ABSOLUTE VALUE EQUATION. UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS. ISSN 1223-7027, 2016, vol. 78, no. 1, p. 25-U338. [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]
--- ZHANG, M. - HUANG, Z.H. - LI, Y.F. The Sparsest Solution to the System of Absolute Value Equations. JOURNAL OF THE OPERATIONS RESEARCH SOCIETY OF CHINA. ISSN 2194-668X, MAR 2015, vol. 3, no. 1, p. 31-51. [WOS]
--- LI, J. - QIAO, B.M. a novel Differential Evolution algorithm with K-Means and Simplex Search Method for Absolute Value Equations. 2015 11TH INTERNATIONAL CONFERENCE ON COMPUTATIONAL INTELLIGENCE AND SECURITY (CIS). 2015, p. 266-269. [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]
--- GUO, P. - WU, S.L. - LI, C.X. On the SOR-like iteration method for solving absolute value equations. APPLIED MATHEMATICS LETTERS. ISSN 0893-9659, NOV 2019, vol. 97, p. 107-113. [WOS]
--- HUANG, B.H. - MA, C.F. Convergent conditions of the generalized Newton method for absolute value equation over second order cones. APPLIED MATHEMATICS LETTERS. ISSN 0893-9659, JUN 2019, vol. 92, p. 151-157. [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]
--- RAHPEYMAII, F. - AMINI, K. - ALLAHVIRANLOO, T. - MALKHALIFEH, M.R. A new class of conjugate gradient methods for unconstrained smooth optimization and absolute value equations. CALCOLO. ISSN 0008-0624, MAR 2019, vol. 56, no. 1. [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]
--- LIAN, Y.Y. - LI, C.X. - WU, S.L. Weaker convergent results of the generalized Newton method for the generalized absolute value equations. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. ISSN 0377-0427, AUG 15 2018, vol. 338, p. 221-226. [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]
--- 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]
--- NOOR, M.A. - NOOR, K.I. - BATOOL, S. ON GENERALIZED ABSOLUTE VALUE EQUATIONS. UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS. ISSN 1223-7027, 2018, vol. 80, no. 4, p. 63-70. [WOS]
--- ACHACHE, M. - HAZZAM, N. SOLVING ABSOLUTE VALUE EQUATIONS VIA COMPLEMENTARITY AND INTERIOR-POINT METHODS. JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS. ISSN 2052-532X, 2018. [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]
--- GU, X.M. - HUANG, T.Z. - LI, H.B. - WANG, S.F. - LI, L. TWO CSCS-BASED ITERATION METHODS FOR SOLVING ABSOLUTE VALUE EQUATIONS. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION. ISSN 2156-907X, NOV 2017, vol. 7, no. 4, p. 1336-1356. [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]
--- WANG, H.J. - CAO, D.X. - LIU, H. - QIU, L. Numerical validation for systems of absolute value equations. CALCOLO. ISSN 0008-0624, SEP 2017, vol. 54, no. 3, p. 669-683. [WOS]
--- LI, J. - LIU, J. - WANG, M.L. - WEI, F. A new algorithm for computing all solutions of an absolute value equation. 2017 13TH INTERNATIONAL CONFERENCE ON COMPUTATIONAL INTELLIGENCE AND SECURITY (CIS). 2017, p. 381-384. [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]
Permanent Link: http://hdl.handle.net/11104/0012497