MA 784 House Rules (also available in pdf or postscript)

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MA 784 General Information
References , Syllabus , ma784 home page

• Instructor: C. T. Kelley
  Office: HA 331, (919) 515-7163 (office), (919) 515-3798 (FAX)
  Office Hours: TBA
  
  
• Books: Free downloads from the publisher
  • Iterative Methods for Linear and Nonlinear Equations, Kelley, SIAM, 1995
  • Iterative Methods for Optimization . Kelley, SIAM, 1999
  • Prerequisites: MA 580 good FORTRAN, C, or MATLAB programming skills, and a knowledge of advanced calculus at the level of MA 511 or MA 512 .
  • Grade: Homework and programs (40%), presentation (60%). I require that the homework be typeset (some form of TeX, WORD, ...).
  • We will use the NCSU UNIX workstations. Students are expected to be familiar with the EOS/UNITY environment.
  • Languages: MATLAB (preferred), FORTRAN, C. We offer significant software support for MATLAB.

MA 784 References
General Information , Syllabus , ma784 home page

• James W. Demmel, Applied Numerical Linear Algebra, James W. Demmel, SIAM, 1997.

• J. E. DENNIS AND R. B. SCHNABEL, Numerical Methods for Nonlinear Equations and Unconstrained Optimization, no. 16 in Classics in Applied Mathematics, SIAM, Philadelphia, 1996.

• G. H. GOLUB AND C. G. VANLOAN , Matrix Computations, Johns Hopkins University Press, Baltimore, 1983.

• A. GREENBAUM, Iterative Methods for Solving Linear Systems, no. 17 n SIAM Frontiers in Applied Mathematics, SIAM, Philadelphia, 1997.

• D. J. Higham and N. J. Higham, MATLAB Guide, SIAM, Philadelphia, 2000.

• E. ISAACSON AND H. B. KELLER , Analysis of numerical methods, Wiley, New York, 1966.

• L. KANTOROVICH AND G. AKILOV, Functional Analysis, Pergamon Press, New York, second ed., 1982.

• C. T. KELLEY , Iterative Methods for Linear and Nonlinear Equations, no. 16 in SIAM Frontiers in Applied Mathematics, SIAM, Philadelphia, 1995.

• C. T. KELLEY , Iterative Methods for Optimization , no. 18 in SIAM Frontiers in Applied Mathematics, SIAM, Philadelphia, 1999.

• C. T. KELLEY , Solving Nonlinear Equations with Newton's Method, no. 1 in SIAM series on Fundamental Algorithms for Numerical Calculations, 2003.

• J. M. ORTEGA AND W. C. RHEINBOLDT, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.

• K. SIGMON, MATLAB Primer, Fourth Edition, CRC Press, Boca Raton, FL, 1994.

• G. W. STEWART , Introduction to matrix computations, Academic Press, New York, 1973.

• L. N. TREFETHEN and D. BAU, Numerical Linear Algebra , SIAM, Philadelphia, 1996.

MA784 Syllabus
General Information , References , ma784 home page

• Week 1-2: Nonlinear equations/optimization in one variable.
• Week 2-3: Review of advanced calculus and numerical linear algebra.
• Week 3-6: Newton's method and variations in several variables. Newton Iterative Methods.
• Weeks 6-7: Broyden's method, proof of superlinear convergence.
• Week 9: Unconstrained Optimization, Newton's method for unconstrained optimization.
• Week 10-11: Globally convergent variations of Newton's method.
• Week 11-13: Nonlinear least squares, Quasi-Newton methods for unconstrained optimization.
• Weeks 13-14: Student presentations.