Numerical Methods for Nonlinear Equations
and Unconstrained Minimization
MA 590 (Special Topics)
Fall 2009

Resources


MATLAB references

Kermit Sigmon's original (free) MATLAB Primer (PostScript or PDF).
This is dated in some respects but still a good introduction to most of the basics. The PDF file looks fuzzy on the screen but prints out well.

Kermit Sigmon and Timothy A. Davis, MATLAB Primer (7th Edition). This is the current commercial version, available from Chapman & Hall/CRC Press for $21.95 plus shipping. It is considerably more up-to-date and inclusive than the free primer.

Supplementary references

    Slobodan Pajic's MA 590 notes from fall 2006.

    Short course notes

H. F. Walker, Numerical Methods for Nonlinear Equations, WPI Mathematical Sciences Department Tech. Rep. MS-02-03-18, March, 2002.
General references
  1. A. R. Conn, N. I. M. Gould, and P. L. Toint, Trust-Region Methods, MPS-SIAM Series on Optimization, SIAM, Philadelphia, 2000.
  2. J. E. Dennis, Jr., and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, SIAM Classics in Applied Mathematics, Vol. 16, SIAM, Philadelphia,1996. Originally published in the Prentice Hall Series in Automatic Computation, Prentice Hall, Englewood Cliffs, NJ, 1983.
  3. G. E. Forsythe, M. A. Malcolm, and C. B. Moler, Computer Methods for Mathematical Computations, Prentice Hall Series in Automatic Computation, Prentice Hall, Englewood Cliffs, NJ, 1977.
  4. W. J. F. Govaerts, Numerical Methods for Bifurcations of Dynamical Equilibria, SIAM, Philadelphia, 2000.
  5. C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations, SIAM Frontiers in Applied Mathematics, SIAM, Philadelphia, 1995.
  6. _________, Iterative Methods for Optimization, SIAM Frontiers in Applied Mathematics, SIAM, Philadelphia, 1999.
  7. _________, Solving Nonlinear Equations with Newton's Method, SIAM Fundamentals of Algorithms,  SIAM, Philadelphia, 2003.
  8. J. Nocedal and S. J. Wright, Numerical Optimization, Springer Series in Operations Research, Springer, New York, 1999.
  9. J. M. Ortega and W. C. Rheinboldt, Iterative Solution on Nonlinear Equations in Several Variables, Academic Press, New York, 1970.
  10. A. Ralston and P. Rabinowitz, A First Course in Numerical Analysis (2nd Edition), McGraw-Hill, New York, 1978.
  Other books and papers (to be added to during the course)
  1. E. L. Allgower and K. Georg, Continuation and path following, Acta Numerica 1993, Cambridge University Press, Cambridge, England, pp. 1-64.
  2. E. L. Allgower, K. Bohmer, F. A. Potra, and W. C. Rheinboldt, A mesh-independence principle for operator equations and their discretizations, SIAM J. Numer. Anal., 23 (1986), pp. 160-169.
  3. A. D. Bazykin, Mathematical biophysics of interacting populations, Nauka, Moscow, 1985. (In Russian.)
  4. ___________, Nonlinear Dynamics of Interacting Populations, World Scientific series on Nonlinear Science, World Scientific, Singapore, 1998.
  5. R. P. Brent, An algorithm with guaranteed convergence for finding a zero of a function, The Computer Journal, 14 (1971), pp. 422-425.
  6. _________, Algorithms for Minimization without Derivatives, Prentice Hall Series in Automatic Computation, Prentice Hall, Englewood Cliffs, NJ, 1973.
  7. A. Curtis, M. J. D. Powell, and J. K. Reid, On the estimation of sparse Jacobian matrices, J. Inst. Math. Appl., 13 (1974), pp. 117-120.
  8. T. J. Dekker, Finding a zero by means of successive linear interpolation, in B. Dejon and P. Henrici (eds.), Constructive Aspects of the Fundamental Theorem of Algebra, Wiley-Interscience, New York, 1969.
  9. M. Pernice and H. F. Walker, NITSOL: a Newton iterative solver for nonlinear systems, SIAM J. Sci. Comput., 19 (1998), pp. 302-318.
  10.  V. E. Shamanskii, A modification of Newton's method, Ukran. Math. Xh., 19 (1967), pp. 133-138. (In Russian.)