MA 784 House Rules
MA 784 House Rules (also available in
pdf
MA 784 General Information
References , Syllabus ,
ma784 home page
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Instructor:
C. T. Kelley
Office: SAS 3234, (919) 515-7163 (office), (919) 515-3798 (FAX)
Office Hours: TBA
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Books: Free downloads from the publisher
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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.
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James W. Demmel,
Applied Numerical Linear Algebra,
James W. Demmel, SIAM, 1997.
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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.
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G. H. GOLUB
AND
C. G. VANLOAN , Matrix Computations, Johns Hopkins
University Press, Baltimore, 1983.
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A. GREENBAUM,
Iterative Methods for Solving Linear Systems,
no. 17 n SIAM Frontiers in Applied Mathematics, SIAM,
Philadelphia, 1997.
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D. J. Higham and
N. J. Higham,
MATLAB Guide, SIAM, Philadelphia, 2000.
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E. ISAACSON AND
H. B. KELLER ,
Analysis of numerical methods, Wiley, New York, 1966.
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L. KANTOROVICH AND G. AKILOV, Functional Analysis, Pergamon Press,
New York, second ed., 1982.
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C. T. KELLEY ,
Iterative Methods for Linear and Nonlinear
Equations, no. 16 in SIAM Frontiers in Applied Mathematics, SIAM,
Philadelphia, 1995.
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C. T. KELLEY ,
Iterative Methods for Optimization ,
no. 18 in SIAM Frontiers in Applied Mathematics, SIAM,
Philadelphia, 1999.
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C. T. KELLEY ,
Solving Nonlinear Equations with Newton's Method,
no. 1 in SIAM series on Fundamental Algorithms for Numerical Calculations,
2003.
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J. M. ORTEGA
AND W. C. RHEINBOLDT, Iterative Solution of Nonlinear
Equations in Several Variables, Academic Press, New York, 1970.
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K. SIGMON, MATLAB Primer, Fourth Edition, CRC Press, Boca Raton,
FL, 1994.
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G. W. STEWART ,
Introduction to matrix computations, Academic Press,
New York, 1973.
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L. N. TREFETHEN
and D. BAU,
Numerical Linear Algebra ,
SIAM, Philadelphia, 1996.
In response to
requests from the students and/or recent advances in the subject,
this syllabus may change as the course progresses.
- 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.
Last modified: October 3, 2010.
C. T. Kelley
,
Tim_Kelley@ncsu.edu