f:\693\m693a.f94
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        Math 693a - Advanced Numerical Analysis
                        Fall '94
                    Dr. Kris Stewart
                 (stewart@cs.sdsu.edu)

Course:   MW: 5-6:15/BA 259

Office Hours:  MW 3:30-5 (the best way to contact me is
                          via electronic mail to stewart)

Note: the first 4 Wednesdays of the fall semester, the
      class and office hours will be held in BA 110
      the new Xterminal Lab.

Text: Scientific Computing: An Introduction with
      Parallel Computing, Gene Golub and James M. Ortega
      Academic Press, 1993

      An optional text: An Intro. to Numerical Analysis
      (2nd Ed.) by K.E. Atkinson (Wiley & Sons) is an
      excellent background reference, but was mistakenly
      listed in the bookstore at Required not Optional. I
      apologize for this, but I would recommend having the
      book since we will refer to it for fundamental topics
      often.

This course will involve the study of the mathematical
background of algorithms to solve the major problems from
science using the computer.  There will be significant
computational experiments, involving programming in C or
Fortan or MATLAB using ucssun1, as well as written reports
detailing the problem statement, goals, results and
interpretation of the results.

Optionally, students may elect to work on the Cray C90 or
the Intel Paragon at the San Diego Supercomputer, but this
is not required and is only suggested for the "adventuresome".
This will be most appropriate in the second semester of the
course.

Much of the programming in the computational experiments
will be based on initial running examples available from the
instructor and using publicly available software packages.

Extensive use of the Internet will be made. Introductory
lectures on electronic mail, ftp, gopher and other
available info-servers will be covered in the first
few weeks in the Xterm Lab (BA 110) to ensure that all
students have access to this valuable resource.

The first semester will focus on Integral Equations,
Optimization and Least Squares using extensive handouts
from the instructor.

The second semester of this sequence (Math 693b) will
focus on differential equations (both ordinary and
partial).


Calendar

Week 1:
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Aug. 29 - Lecture Chapter 1 - Golub & Ortega
                  "The World of Scientific Computing"
          Handout "An Overview of Scientiif Computing",
                  by Lloyd Fosdick and Elizabeth Jessup
          Handout first "homework" (review linear algebra)
          You should read Chapter 2 - Linear Algebra

Aug. 31 - (lecture held in BA 110) Using the Internet
          for information and electronic mail.
          Work through solutions of first "homework"
          Handout second "homework" (review finite differences)

Week 2:
-------

Sept. 7 - (lecture held in BA 110)
          Work through solutions of second "homework"

Week 3:
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Sept. 12  Lecture Chapter 6 - Direct Soln of Linear Equations
          Handout first computational experiment - Numerical
            Solution of Fredholm Integral Equation (of second kind)
            Due - October 17 (using the wandt.for code for
            the nodes) - Atkinson p. 575 #4 (and class handout)

Sept. 14 (lecture held in BA 110)

Week 4:
-------
Sept. 19 Lecture covering Integral Equations handout
Sept. 21 Lecture covering Integral Equations handout (no lab)

Week 5:
-------
Sept. 26 Lecture Chapter 4 - Polynomial Approximation
         4.1 Taylor Series, Interpolation and Splines
         4.2 Least Squares Approximation
Sept. 28 4.3 Applications to Root-Finding

Week 6:
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Oct. 3   Lecture 2.10, 2.11, 2.12 Atkinson (Nonlinear
         Systems of Equations)
         Distribution Optimization Handouts

Oct. 5   Lecture handouts on Optimization  taken from the text:
         Dennis and Schnable - "Numerical Methods for Unconstrained
         Optimization and Nonlinear Equations", Prentice-Hall, 1983

Week 7:
-------

Oct. 10  Continue lectures on nonlinear equations
Oct. 12

Week 8:
-------

Oct. 17 First Computational Experiment (Integral Equations) due
Oct. 19 Lab experiments in BA 110
        Handout second Computational Experiment for
        Nonlinear System Solving - use MINPACK - due Nov. 7

Week 9:
-------

Oct. 24 Lecture material handout for Nonlinear Least Squares
        (NLLS)
Oct. 26

Week 10:
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Oct. 31 Continue lectures on NLLS
Nov. 2

Week 11:
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Nov. 7  Computational Experiment on Nonlinear System Solving
Nov. 9  Handout final Computational Experiment - Nonlinear
        Least Squares - due Dec. 7


Week 12:
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Nov. 14 Midterm 1 (covering linear and nonlinear systems)
Nov. 16 Lab Experiments in BA 110 involving NLLS

Week 13:
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Nov. 21 Application to Parallel Computing - Chapter 3 (G&O)
        3.1 Parallel and Vector Computers
Nov. 23 3.2 Basic Concepts of Parallel Computing
        3.3 Matrix Multiplication

Week 14:
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Nov. 28 Ch. 7 - Parallel Direct Methods
        7.1 Basic Methods
Nov. 30 7.2 Other Organizations or Factorization
        7.3 Banded and Tridiagonal Systems

Week 15:
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Dec. 5   Handout take home final exam
Dec. 7   Nonlinear Least Squares Computational Experiment
         due

Final Exam:  Saturday, Dec. 17 8-10am
             Since this is a take home exam, it will be due
             on Friday, Dec. 16, turned into the Department office
             or placed in the U.S. Mail with postmark of Dec. 17