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Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 4))

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Abstract

Eigenvalue problems are at the base of many scientific and technological issues. They appear at the root of stability problems, differential equations, either ordinary or partial, Mechanics of continuous media, etc.

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References

  1. D.R. Anderson, D.J. Sweeney, T.A. Williams, Linear Programming for Decision Making (West Publishing, New York, 1974)

    Google Scholar 

  2. P.M. Anselone, L.B. Rall, The solution of characteristic value-vector problems by Newton’s method. Numer. Math. 11, 38–45 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  3. M. Avriel, Nonlinear Programming. Analysis and Methods (Dover Publications, Mineola, 2003)

    Google Scholar 

  4. E.M.L. Beale, Numerical Methods in Nonlinear Programming, ed. by J. Abadie (North Holland Publishing, Amsterdam, 1967)

    Google Scholar 

  5. J.T. Betts, Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, 2nd edn. SIAM’s Advances in Design and Control (2010)

    Google Scholar 

  6. J.F. Bonnans, J.Ch. Gilbert, C. Lemarchal, C.A. Sagastizbal, Numerical Optimization: Theoretical and Practical Aspects (Springer, New York, 2006)

    MATH  Google Scholar 

  7. F. Chatelin, Eigenvalues of Matrices (Wiley, Chichester, 1995)

    Google Scholar 

  8. K.A. Cliffe, T.J. Garratt, A. Spence, Eigenvalues of block matrices arising from problems in Fluid Mechanics. SIAM J. Matrix Anal. Appl. 15(4), 1310–1318 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  9. R. Cottle, E. Johnson, R. Wets, George B. Dantzig (1914–2005). Not. AMS 54(3), 344–369 (2007)

    Google Scholar 

  10. G.B. Dantzig, Linear Programming and Extensions (Princeton University Press, Princeton, 1963)

    MATH  Google Scholar 

  11. V.N. Faddeeva, Computational Methods of Linear Algebra (Dover Publications, New York, 1959)

    MATH  Google Scholar 

  12. J. Franklin, Methods of Mathematical Economics (Springer, New York, 1980)

    Book  MATH  Google Scholar 

  13. H. Goldstein, Classical Mechanics (Addison-Wesley, Readings, 1981)

    Google Scholar 

  14. G.H. Golub, Ch.F. Van Loan, Matrix Computations, 2nd edn. (Johns Hopkins, Baltimore, 1989)

    MATH  Google Scholar 

  15. J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vectors Fields (Springer, New York, 1983)

    Google Scholar 

  16. E. Hairer, C. Lubich, G. Wanner, Geometric Numerical Integration, 2nd edn. (Springer, New York, 2006)

    MATH  Google Scholar 

  17. S. Jiménez, L. Vázquez, Analysis of a nonlinear Klein-Gordon equation. Appl. Math. Comput. 35, 61–94 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  18. S. Jiménez, P. Pascual, C. Aguirre, L. Vázquez, A panoramic view of some perturbed nonlinear wave equations. Int. J. Bifurcat. Chaos 14(1), 1–40 (2004)

    Article  MATH  Google Scholar 

  19. S. Jiménez, L. Vázquez, A dynamics approach to the computation of eigenvectors of matrices. J. Comput. Math. 23(6), 657–672 (2005)

    MathSciNet  Google Scholar 

  20. N. Karmarkar, A new Polynomial-time algorithm for linear programming. Combinatorica 4(4), 373–395 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  21. L.G. Khachiyan, A polynomial Algorithm in Linear Programming. Dokl. Akad. Nauk SSSR, 244(S), 1093–1096 (1979), translated in Soviet Mathematics Doklady 20(1), 191–194 (1979)

    Google Scholar 

  22. V.V. Konotop, L. Vázquez, Nonlinear Random Waves (World Scientific, Singapore, 1994). See also references [379], [403], [326], [404] and [191], therein.

    Google Scholar 

  23. M.C. Navarro, H. Herrero, A.M. Mancho, A. Wathen, Efficient solution of a generalized eigenvalue problem arising in a thermoconvective instability. Comm. Comput. Phys. 3(2), 308–329 (2008)

    MathSciNet  MATH  Google Scholar 

  24. L. Perko, Differential Equations and Dynamical Systems, 3rd edn. (Springer, New York, 2001)

    MATH  Google Scholar 

  25. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, J.G.P. Barnes, Numerical Recipes in C. The Art of Scientific Computing, 2nd edn. (Cambridge University Press, Cambridge, 1995)

    Google Scholar 

  26. M. Rossignoli, The Complete Pinball Book: Collecting the Game & Its History (Schiffer Publishing, Atglen, 2011)

    Google Scholar 

  27. F. Santos, A counterexample to the Hirsch conjecture, arXiv:1006.2814 (2010)

    Google Scholar 

  28. J. Stoer, R. Burslisch, Introduction to Numerical Analysis, 2nd edn. (Springer, New York, 2002)

    MATH  Google Scholar 

  29. W.A. Strauss, L. Vázquez, Numerical solutions of a nonlinear Klein-Gordon equation. J. Comput. Phys. 28, 271–278 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  30. J. Todd, The condition number of the finite segment of the Hilbert matrix. Natl. Bur. Stand. Appl. Math. Ser. 39, 109–116 (1954)

    MathSciNet  Google Scholar 

  31. L. Vázquez, S. Jiménez, Analysis of a mechanical solver for linear systems of equations. J. Comput. Math. 19(1), 9–14 (2001)

    MathSciNet  MATH  Google Scholar 

  32. L. Vázquez, J.L. Vázquez-Poletti, A new approach to solve systems of linear equations. J. Comput. Math. 19(4), 445–448 (2001)

    MathSciNet  MATH  Google Scholar 

  33. L. Vázquez, J.L. Vázquez-Poletti, A mechanical approach for linear programming. http://www.uni-bielefeld.de/ZiF/complexity; ZiF Preprint 2001/066 (2001)

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Vázquez, L., Jiménez, S. (2013). Eigenvalue Problems. In: Newtonian Nonlinear Dynamics for Complex Linear and Optimization Problems. Nonlinear Systems and Complexity, vol 4. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5912-5_4

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  • DOI: https://doi.org/10.1007/978-1-4614-5912-5_4

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