PEPACK

We describe a software package for computing the numerical solution of palindromic and even eigenvalue problems using the Pencil Laub Trick. The package contains Fortran 77 routines which reduce real and complex palindromic and even pairs of matrices to anti-triangular form. We give explicit descriptions how to use the package including an example.


References in zbMATH (referenced in 25 articles )

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  1. Malyshev, Alexander; Sadkane, Miloud: Computing the distance to continuous-time instability of quadratic matrix polynomials (2020)
  2. De Terán, Fernando; Dopico, Froilán M.; Mackey, D. Steven; Perović, Vasilije: Quadratic realizability of palindromic matrix polynomials (2019)
  3. Dopico, Froilán M.; Pérez, Javier; van Dooren, Paul: Structured backward error analysis of linearized structured polynomial eigenvalue problems (2019)
  4. Zhao, Kang; Cheng, Lizhi; Liao, Anping; Li, Shengguo: On inverse eigenvalue problems of quadratic palindromic systems with partially prescribed eigenstructure (2019)
  5. Zhao, Kang; Cheng, Lizhi; Liao, Anping: Updating (\star)-palindromic quadratic systems with no spill-over (2018)
  6. Batzke, Leonhard: Generic rank-two perturbations of structured regular matrix pencils (2016)
  7. Mehrmann, Volker; Xu, Hongguo: Structure preserving deflation of infinite eigenvalues in structured pencils (2015)
  8. Batzke, Leonhard: Generic rank-one perturbations of structured regular matrix pencils (2014)
  9. Benner, Peter; Voigt, Matthias: Spectral characterization and enforcement of negative imaginariness for descriptor systems (2013)
  10. Bini, Dario A.; Noferini, Vanni: Solving polynomial eigenvalue problems by means of the Ehrlich-Aberth method (2013)
  11. Mackey, D. Steven; Mackey, Niloufer; Mehl, Christian; Mehrmann, Volker: Skew-symmetric matrix polynomials and their Smith forms (2013)
  12. Mehrmann, Volker; Poloni, Federico: A generalized structured doubling algorithm for the numerical solution of linear quadratic optimal control problems (2013)
  13. Al-Ammari, Maha; Tisseur, Françoise: Standard triples of structured matrix polynomials (2012)
  14. Gamkrelidze, R. V. (ed.); Mikhalev, A. V. (ed.); Sadovnichy, V. A. (ed.): Proceedings of the international algebraic conference dedicated to the 80th anniversary of the Department of Higher Algebra of the Faculty of Mechanics and Mathematics of Moscow State University and the 70th birthday of Professor A. V. Mikhalev, Moscow, Russia, November 15--18, 2010. Part 3. Transl. from the Russian. (2012)
  15. Adhikari, Bibhas; Alam, Rafikul: On backward errors of structured polynomial eigenproblems solved by structure preserving linearizations (2011)
  16. Brüll, Tobias: Checking dissipativity of linear behavior systems given in kernel representation (2011)
  17. De Terán, Fernando; Dopico, Froilán M.; Mackey, D. Steven: Palindromic companion forms for matrix polynomials of odd degree (2011)
  18. Mackey, D. Steven; Mackey, Niloufer; Mehl, Christian; Mehrmann, Volker: Smith forms of palindromic matrix polynomials (2011)
  19. Reis, Timo: Lur’e equations and even matrix pencils (2011)
  20. Mackey, D. Steven; Mackey, Niloufer; Mehl, Christian; Mehrmann, Volker: Jordan structures of alternating matrix polynomials (2010)

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