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2011 | 9 | 5 | 1171-1184
Tytuł artykułu

Interval algorithm for absolute value equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We investigate the absolute value equations Ax−|x| = b. Based on ɛ-inflation, an interval verification method is proposed. Theoretic analysis and numerical results show that the new proposed method is effective.
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
5
Strony
1171-1184
Opis fizyczny
Daty
wydano
2011-10-01
online
2011-07-26
Twórcy
autor
autor
autor
Bibliografia
  • [1] Alefeld G., Mayer G., Interval Analysis: Theory and Applications, J. Comput. Appl. Math., 2000, 121, 421–464 http://dx.doi.org/10.1016/S0377-0427(00)00342-3
  • [2] Caccetta L, Qu B., Zhou G., A globally and quadratically convergent method for absolute value equations, Comput. Optim. Appl., 2011, 48(1), 45–58 http://dx.doi.org/10.1007/s10589-009-9242-9
  • [3] Chen X., Qi L., Sun D., Global and superlinear convergence of the smoothing Newton method and its application to general box constrained variational inequalities, Math. Comp., 1998, 67(222), 519–540 http://dx.doi.org/10.1090/S0025-5718-98-00932-6
  • [4] Clarke F.H., Optimization and Nonsmooth Analysis, 2nd ed., Classics Appl. Math., 5, Society for Industrial and Applied Mathematics, Philadelphia, 1990
  • [5] Mangasarian O.L, Absolute value programming, Comput. Optim. Appl, 2007, 36(1), 43–53 http://dx.doi.org/10.1007/s10589-006-0395-5
  • [6] Mangasarian O.L, A generalized Newton method for absolute value equations, Optim. Lett., 2009, 3(1), 101–108 http://dx.doi.org/10.1007/s11590-008-0094-5
  • [7] Mangasarian O.L, Knapsack feasibility as an absolute value equation solvable by successive linear programming, Optim. Lett, 2009, 3(2), 161–170 http://dx.doi.org/10.1007/s11590-008-0102-9
  • [8] Mangasarian O.L, Meyer R.R., Absolute value equations, Linear Algebra Appl., 2006, 419(2–3), 359–367 http://dx.doi.org/10.1016/j.laa.2006.05.004
  • [9] Mayer G., Epsilon-inflation in verification algorithms, J. Comput. Appl. Math., 1995, 60(1–2), 147–169 http://dx.doi.org/10.1016/0377-0427(94)00089-J
  • [10] Moore R.E., A test for existence of solutions to nonlinear systems, SIAM J. Numer. Anal., 1977, 14(4), 611–615 http://dx.doi.org/10.1137/0714040
  • [11] Moore R.E., Methods and Applications of Interval Analysis, SIAM Stud. Appl. Math., 2, Society for Industrial and Applied Mathematics, Philadelphia, 1979
  • [12] Prokopyev O., On equivalent reformulations for absolute value equations, Comput. Optim. Appl., 2009, 44(3), 363–372 http://dx.doi.org/10.1007/s10589-007-9158-1
  • [13] Qi L., Sun D., Smoothing functions and smoothing Newton method for complementarity and variational inequality problems, J. Optim. Theory Appl., 2002, 113(1), 121–147 http://dx.doi.org/10.1023/A:1014861331301
  • [14] Rohn J., Systems of linear interval equations, Linear Algebra Appl., 1989, 126, 39–78 http://dx.doi.org/10.1016/0024-3795(89)90004-9
  • [15] Rohn J., A theorem of the alternatives for the equation Ax + B|x| = b, Linear Multilinear Algebra, 2004, 52(6), 421–426 http://dx.doi.org/10.1080/0308108042000220686
  • [16] Rohn J., Description of all solutions of a linear complementarity problem, Electron. J. Linear Algebra, 2009, 18, 246–252
  • [17] Rohn J., An algorithm for solving the absolute value equation, Electron. J. Linear Algebra, 2009, 18, 589–599
  • [18] Rohn J., On unique solvability of the absolute value equation, Optim. Lett., 2009, 3(4), 603–606 http://dx.doi.org/10.1007/s11590-009-0129-6
  • [19] Rohn J., A residual existence theorem for linear equations, Optim. Lett., 2010, 4(2), 287–292 http://dx.doi.org/10.1007/s11590-009-0160-7
  • [20] Rump S.M., Kleine Fehlerschranken bei Matrixproblemen, Ph.D. thesis, Universität Karlsruhe, 1980
  • [21] Rump S.M., New results on verified inclusions, In: Accurate Scientific Computations, Bad Neuenahr, 1985, Lecture Notes in Comput. Sci., 235, Springer, Berlin, 1986, 31–69
  • [22] Rump S.M., On the solution of interval linear systems, Computing, 1992, 47(3–4), 337–353 http://dx.doi.org/10.1007/BF02320201
  • [23] Rump S.M., Verified solution of large systems and global optimization problems, J. Comput. Appl. Math., 1995, 60(1–2), 201–218 http://dx.doi.org/10.1016/0377-0427(94)00092-F
  • [24] Rump S.M., INTLAB-INTerval LABoratory, In: Developments in Reliable Computing, Budapest, September 22–25, 1998, Kluwer, Dordrecht, 1999, 77–104
  • [25] Zhang C, Wei Q.J., Global and finite convergence of a generalized Newton method for absolute value equations, J. Optim. Theory Appl., 2009, 143(2), 391–403 http://dx.doi.org/10.1007/s10957-009-9557-9
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0067-2
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