Two Estimations of the united solution set to the Interval Unilateral Quadratic Matrix Equations

سال انتشار: 1394
نوع سند: مقاله کنفرانسی
زبان: انگلیسی
مشاهده: 601

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شناسه ملی سند علمی:

NSOECE04_110

تاریخ نمایه سازی: 9 مرداد 1395

چکیده مقاله:

Introducing the interval unilateral quadratic matrix equation, A.X^2+B.X+C=0, we describe some analytical results on its AE-solution sets in which A, B and C are known real interval matrices, while X is the unknown matrix. Then, one sufficient condition for solvability (non emptiness of the united solution set) of the united solution set is given. Two direct methods for estimation of the united solution set of this interval unilateral quadratic matrix equation are proposed. Suggested techniques are based on sensitivity analysis as well as nonlinear programming. Finally, these methods are tested on a number of numerical examples and their results are compared to each other

کلیدواژه ها:

Interval unilateral quadratic matrix equation ، interval arithmetic ، united solution set ، nonlinear programming ، sensitivity analysis

نویسندگان

Tayyebe Haqiri

Ph.D. Student, Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

Mahmoud Mohseni Moghadam

Professor in Applied Mathematics, Mathematics Department, Islamic Azad University, Kerman Branch, Kerman, Iran

Federico Poloni

Assistant Professor, Department of Computer Science, University of Pisa, Pisa, Italy

Azim Rivaz

Assistant Professor, Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

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  • Benner, P. (1991);، Computational Methods for Linear- Quadratic Optimization", Rend. ...
  • Bini, DA.; Latouche, G.; Meini, B. (2005); Numerical Methods for ...
  • Bini, DA.; Meini, B.; Poloni, F. (2008); "From Algebraic Riccati ...
  • Chapra, SC.: Canale, RP. (2010); Numerical Methods for Engineers: 6th ...
  • Davis, G.J. (1981); "Numerical Solution of a Quadratic Matrix Equation", ...
  • Davis, G.J. (1983); "Algorithm 598: An Algorithm to Compute Solvents ...
  • D ehghani- Madiseh, _ Dehghan, M. (2014); "Generalized solution sets ...
  • D ehghani-Madi seh, M.; Hladik, M. (2015); "Efficient Approaches for ...
  • Deif, A.S. (1986); Sensitivity Analysis in Linear Systems, S pringer-Verlag ...
  • Frommer, A.: Hashemi, B. (2009);، 0Verified Computation of Square Roots ...
  • Frommer, A.; Hashemi, B. (2012);، 0Verified error bounds for solutions ...
  • Guo, CH. (2002); _ a Quadratic Matrix Equation Associated with ...
  • Haqiri, T.; Poloni, F. (2015); "Methods for verified solutions to ...
  • Hashemi, B.; Dehghan, M. (2010); "Efficient Computation of Enclosures for ...
  • Hansen, E.; Walster, G.W. (2003); Global Optimization Using Interval Analysis: ...
  • Higham, N.J.; Kim, H.M. (2001); "Solving a Quadratic Matrix Equation ...
  • Kearfott, R.B.; Nakao, M.; Neumaier, A.; Rump, S.; Shary, S.; ...
  • Lancaster, P. and Rodman, L. (1995); Algebraic Riccati Equations, The ...
  • Lancaster, P. (1966); Lambda -Matrices and Vibrating Systems, Pergamon Press, ...
  • Long, J.H., Hu, X.Y. and Zhang, L. (2008); "Improved Newton's ...
  • Moler, C.; Costa, P.J. (1998); Symbolic Math Toolbox Version 2: ...
  • Neumaier, A. (1990); Interval Methods for Systems of Equations, Cambridge ...
  • Poloni, F.; Haqiri, T. (2015); Permuted graph bases for verified ...
  • Seif, N.P.; Hussein, S.A.; Deif, A.S. (1994); :The Interval Sylvester ...
  • Shary, S.P. (2002); _ Technique in Systems Analysis under Interval ...
  • Smith, H.A.; Singh, R.K.; Sorensen, D.C. (1995); Formulation and Solution ...
  • Tisseur, F.; Meerbergen, K. (2001);"The Quadratic Eigenvalue Problem", SIAM Rev ...
  • نمایش کامل مراجع