Numerical Analysis and Approximation I

Days & Times       Room    Instructor      Meeting Dates
------------------------------------------------------------------------
TR noon-1:15pm     AB108   Eric Olson      08/27/2018 - 12/11/2018

Announcements

[16-Dec-2018] Note on Secant Method

[12-Dec-2018] Quiz 2 Answers

[11-Dec-2018] Programming Project 1 Answers

[04-Dec-2018] Quiz 2 Study Guide

• Hand computation of ||A||₁ and ||A||_∞ matrix norms for a given matrix.
• Proof that ||B||₂= ρ(B^TB)^1/2 where ρ(A)=max{ |λ| : λ is an eigenvalue of A }.
• The rest of the problems in Homework 2.

[02-Dec-2018] Programming Project 2

[01-Dec-2018] Quiz 1 Answers

[20-Nov-2018] Quiz 1 Study Guide

• Statement of Taylor's theorem.
• Proof of Taylor's theorem.
• Description of Newton's method.
• Proof of quadratic convergence of Newton's method.
• Homework on roudning error.
• Description of power method for finding the largest eigenvalue in magnitude and corresponding eigenvector.
• Proof that the power method converges in the case where A is a positive semindefinite matrix.
• Homework on matrix norms Section 4.4 problems 1,2,3,4,5.
• Programming project on Newton's method, the secant method, Steffenson's method and secant-like approximation of Steffenson's method.

[09-Oct-2018] Programming Project 1

[25-Sep-2018] Files for Writing a Report

[12-Sep-2018] Handouts and Lecture Notes

[04-Sep-2018] Video Homework 1

• In what country does John Gustafson currently live?
• Show that the dot product of (3.2e8,1,-1,8.0e7) with (4.0e7,1,-1,-1.6e8) is exactly 2.
• What are the advantages of posits compared to floating point numbers?
• Predict when, if ever, hardware that implements posit arithemtic will be available for student use in the UNR computing labs. Explain your reasoning.

Course Information

Instructor:

Eric Olson

email:

ejolson at unr edu

Office:

Monday, Wednesday and Thursday 1pm DMS 238 and by appointment.

Homepage:

http://fractal.math.unr.edu/~ejolson/701

Required Texts:

David Kincaid, Ward Cheney, Numerical Analysis: Mathematics of Scientific Computing, 3rd Edition, American Mathematical Society, 2002.

Kendall Atkinson and Weimin Han, Theoretical Numerical Analysis: A Functional Analysis Framework, 3rd Edition, Spring, 2009.

Additional Resources

Brian Kernighan, Dennis Ritchie, C Programming Language, 2nd Edition, Prentice Hall, 1988.

Brian Kernighan, Rob Pike, The Unix Programming Environment, 1st Edition, 1984.

Robert Glassey, Numerical Computation Using C, Academic Press, 1993

Class Handouts and Lecture Notes

1. Introduction
2. Chapter 1
3. Chapter 2
4. Chapter 3
5. Chapter 1

Internet Resources

• Netlib Repository
• Gnuplot
• Automatically Tuned Linear Algebra Software

Extra Credit

Grading

    2 Exams                   20 points each
    2 Homework Assignments    30 points each
    2 Programming Projects    30 points each
    1 Final Exam              40 points
   ------------------------------------------
                             200 points total

This is an upper-division mathematics class class.  Exams and quizzes
will be interpreted according to the following grading scale:

    Grade        Minimum Percentage
      A                 85 %
      B                 70 %
      C                 60 %
      D                 50 %

The instructor reserves the right to give +/- grades and higher grades
than shown on the scale if he believes they are warranted.

Quizzes, Exams and Homework

• Homework #1 Section 2.2 Problems 1,2,3,4,5,11,16,20,22
• Quiz 1 (answers)
• Homework #2 Section 4.4 Problems 1,2,3,4,5,17,18,19,33,39

Final Exam

Equal Opportunity Statement

Academic Conduct