MA 784 House Rules
MA 784 House Rules (also available in
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MA 784 General Information
References , Syllabus ,
ma784 home page

Instructor:
C. T. Kelley
Office: SAS 3234, (919) 5157163 (office), (919) 5153798 (FAX)
Office Hours: TBA

Books: Free downloads from the publisher

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.

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.
In response to
requests from the students and/or recent advances in the subject,
this syllabus may change as the course progresses.
 Week 12: Nonlinear equations/optimization in one variable.
 Week 23: Review of advanced calculus and numerical linear algebra.
 Week 36: Newton's method and variations in several variables.
Newton Iterative Methods.
 Weeks 67: Broyden's method, proof of superlinear convergence.
 Week 9: Unconstrained Optimization, Newton's method
for unconstrained optimization.
 Week 1011: Globally convergent variations of Newton's method.
 Week 1113: Nonlinear least squares,
QuasiNewton methods for unconstrained optimization.
 Weeks 1314: Student presentations.
Last modified: October 3, 2010.
C. T. Kelley
,
Tim_Kelley@ncsu.edu