Mark J. Pekker (formerly Mark J. Friedman)
Mathematical Sciences Department
University of Alabama in Huntsville
Huntsville, AL 35899
Tel: (256) 824-6470
Fax: (256) 824-6173
Teaching Schedule for Spring 2014
MA 614-01 MW 2:20-3:40, 158 SC.
MA 201-03 MW 5:30 - 7:30, 207 SC
Office Hours: MW: 10:00 - 11:00, 3:40 - 5:10, 7:30 - 8:00 or by appointment.
- Ph.D. (Mathematics), Cornell University, 1982
- M.A. (Mathematics), Cornell University, 1981
- M.S. (Physics/Mathematics), Moscow Institute of Physics and Technology, Russia, 1971
- Numerical linear algebra. Development of efficient algorithms and software for continuation of invariant subspaces of large parameter dependent matrices.
- Numerical bifurcation analysis. Development of algorithms and software for bifurcation analysis in large systems, via subspace reduction, and their implementation in MATLAB.
- Applications to science, including computational biology, systems biology, and engineering.
Selected recent publications
- A.I. Fedoseyev, M.J. Friedman, and E.J. Kansa, “Continuation for Nonlinear Elliptic Partial Differential Equations Discretized by the Multiquadric Method”, Int. J. Bifur. & Chaos, 10, No. 2 (2000), 481 - 492. [pdf]
- J. Demmel, L. Dieci, and M. Friedman, “Computing connecting orbits via an improved algorithm for continuing invariant subspaces”, SIAM J. Sci. Comp., 22, No. 1 (2001), 81 - 94. [pdf]
- L. Dieci and M. Friedman, “Continuation of Invariant Subspaces”, Numer. Lin. Alg. Appl. 8 (2001), 317 - 327. [pdf]
- M. Friedman, “An improved detection of bifurcations in large nonlinear systems via the Continuation of Invariant Subspaces algorithm”, Int. J. Bifur. & Chaos 11, No. 8 (2001), 2277-2285. [pdf]
- A.I. Fedoseyev, M. J. Friedman, and E.J. Kansa, “An improved Multiquadric method for nonlinear elliptic partial differential equations via PDE collocation on the boundary”, Comput. Math. Applic., the Special Issue on Radial Basis Functions, 43, Nos (3-5) (2002), 439-455. [pdf]
- D. Bindel, J. Demmel, M. Friedman, Continuation of Invariant Subspaces for Large Bifurcation Problems, in: on-line PROCEEDINGS, SIAM 2003 Conference on Applied Linear Algebra. [pdf]
- D. Bindel, J. Demmel, M. Friedman, W. Govaerts, and Yu.A. Kuznetsov, "Bifurcation analysis of large equilibrium systems in Matlab". In: V.S. Sunderam et al. (eds.) "Proceedings of the International Conference on Computational Science ICCS 2005, Atlanta, GA, USA, May 22-25, 2005, Part I". Springer Verlag Lecture Notes in Computer Science 3514 (2005), 50-57. [pdf]
- B. Sautois, W. Govaerts, M. Friedman, and Yu.A. Kuznetsov, "Continuation of Homoclinic Orbits in Matlab". In: V.S. Sunderam et al. (eds.) "Proceedings of the International Conference on Computational Science ICCS 2005, Atlanta, GA, USA, May 22-25, 2005, Part I". Springer Verlag Lecture Notes in Computer Science 3514 (2005), 263-270. [pdf]
- D. Bindel, J. Demmel, and M. Friedman, “Continuation of Invariant Subspaces in Large Scale Bifurcation Problems”, SIAM J. Sci. Comp. 30, No 2 (March 2008), 637-656. [pdf]
- M. Friedman and W. Qiu, “On the location and continuation of Hopf bifurcations in large-scale problems”, Int. J. Bifur. & Chaos. 18, No 5 (2008), 1589-1597. [pdf]
- J. Hughes and M. Friedman, “A bisection-like algorithm for branch switching at a simple branch point”, J. Sci. Comput. 41, No 2 (2009), 62-69. [pdf]
- De Witte, W. Govaerts, Yu.A. Kuznetsov, and M. Friedman, “Initialization and Continuation of Homoclinic and Heteroclinic Connections in Matlab”, ACM Trans. Math. Software 38, No. 3 (2012), 18:1-18:34.
- Selivanov VA, Friedman M, Schumaker MF, Cascante M, Trucco M, Votyakova TV, 'Multistationary and Oscillatory Modes of Free Radicals Generation by the Mitochondrial Respiratory Chain Revealed by a Bifurcation Analysis, PLoS Comput Biol. 2012, 8(9): e1002700. [pdf]
- D. Bindel, M. Friedman, W. Govaerts, J. Hughes, and Yu.A. Kuznetsov, “Numerical computation of bifurcations in large equilibrium systems in Matlab”, J. Comput. Appl. Math., 261 (2014), 232-248. [pdf]
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