Numerical Analysis and Approximation I

Math 701: Numerical Analaysis and Approximation I

Days & Times 	Room 	Instructor 	Meeting Dates
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MWF 10:00am     AB634   Eric Olson      08/27/2012 - 12/19/2012

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

Supplemental Texts:
J Stoer, R Burlisch, Introduction to Numerical Analysis, 3rd Edition, Springer, 2002.

William Press, Saul Teukolsky, William Vetterling, Brian Flannery, Numerical Recipes, 3rd Edition, Cambridge University Press, 2007.

Roger Peyret, Spectral Methods for Incompressible Viscous Flow, Springer, 2002.

Announcements

[14-Dec-2012] Final and Project 2

The due date for Programming Project 2 has been postponed to December 14 because of the unreliable power in the DMS building. The final exam will be held on Friday, December 14 from 10:15-12:15pm in AB634. It will cover the material from Quiz 1, Quiz 2 and Exam 1 with the following additions:
  1. Gram Schmidt Algorithm
  2. Newton's divided difference formula
  3. Proof of First Lemma on Unitary Matrices on page 267
  4. Proof of Second Lemma on Unitary Matrices on page 267

[10-Dec-2012] Homework 4

Homework 4 is due December 10.

[08-Dec-2012] Saturday Programming Workshop

Due to the unreliable power, I have decided to cancel the computing workshop originally scheduled for this Saturday December 8. I realize the power outage in our building has made it difficult to finish the programming project. If you need extra time, it is fine to turn in the second programming project on Friday, December 14. Please send me email if there was anything you were planning to ask at the workshop. I will answer through email and if desired set up a meeting to discuss things further.

[07-Dec-2012] Exam 1

Exam 1 will be Friday December 7 in class. It will cover all the theorems from Quiz 1 and Quiz 2 plus an additional theorem to be announced from chapter 6 as well as some definitions. Here is a reduced list of theorems, definitions and algorithms to help you study:

Theorems

  1. Proof of Schur's Theorem on page 266

Definitions

  1. Linear order of convergence
  2. Superlinear order of convergence
  3. Quadratic order of convergence
  4. Stable finite difference equation
  5. Error
  6. Absolute error
  7. Relative error
  8. Condition number for a function
  9. Condition number for linear systems
  10. Matrix norm subordinate to a vector norm
  11. Orthogonal matrix
  12. Unitary matrix
  13. Positive definite matrix
  14. Haar subspace

Algorithms

  1. Bisection method
  2. Newton's method
  3. Horner's method
  4. Quadradtic equation
  5. Computation of |A|∞, |A|1 and |A|2 where A is a matrix
  6. QR algorithm of Francis for finding eigenvalues
  7. Shifted QR algorithm of Francis for finding eigenvalues

[01-Dec-2012] Saturday Programming Workshop

There will be no programming workshop this weekend.

[30-Nov-2012] Quiz 2

Quiz 2 will be Friday November 30 in class. It will cover the proof of Theorem 2 on Polynomial Interpolation Error of page 315 as well as the proof of Theorem 5 on Taylor's Theorem with Integral Remainder on page 9.

[28-Nov-2012] Computer Codes From Class

The computer code we wrote in class is available online as well as an improved version of the same code.

[17-Nov-2012] Saturday Programming Workshop

I have reserved DMS 106 from 1pm to 2:30pm on Saturday in the Davidson Mathematical Sciences Building for our class.

[10-Nov-2012] Saturday Programming Workshop

I have reserved DMS 106 from 1pm to 3pm on Saturday in the Davidson Mathematical Sciences Building for our class. If you missed the workshop you may examine the files for November 10.

[05-Nov-2012] Quiz 1

On November 5 will be an in class quiz covering the proofs of 7 theorems.
  1. Theorem 5 part 4 that the spectral norm |A|2=ρ(AT A)1/2 page 294
  2. Fundamental Theorem of Algebra on page 109
  3. Schur's Theorem on page 266
  4. Theorem 1 on A-orthonormal systems page 235
  5. Lemma 1 on minimizing quadratic forms page 232
  6. Quadratic convergence of Newton's method page 84
  7. Theorem 3 on condition number of a matrix page 192

[02-Nov-2012] Programming Project 1

Programming Project 1 will be due November 2. I you find any errors please let me know.

[27-Oct-2012] Saturday Programming Workshop

I have reserved DMS 106 from 1pm to 3pm on Saturday in the Davidson Mathematical Sciences Building for our class. We will discuss parallel programming on multicore SMP computers. If you missed the workshop you may examine the files for October 27.

[20-Oct-2012] Saturday Programming Workshop

I have reserved DMS 106 from 1pm to 3pm on Saturday in the Davidson Mathematical Sciences Building for our class. We discussed reading input data from a file. If you missed the workshop you may examine the files for October 20.

[13-Oct-2012] Saturday Programming Workshop

I have reserved DMS 106 from 1pm to 3pm on Saturday in the Davidson Mathematical Sciences Building for our class. We discussed rounding error and how to call LAPACK from a C program. If you missed the workshop you may examine the files for October 13 and the improvements I made after class.

[06-Oct-2012] Saturday Programming Workshop

I have reserved MIKC 114 from 1pm to 3pm on Saturday in the Mathewson IGT Knowledge Center for our class. We discussed row-major versus column-major ordering and how to create a library that can be used by other programs. If you missed the workshop you may examine the files for October 6.

[29-Sep-2012] Saturday Programming Workshop

I have reserved DMS 106 from 1pm to 3pm on Saturday in the Davidson Mathematical Sciences Building for our class. We discussed how to make a graph using gnuplot. If you missed the workshop you may examine the files for September 29 and the improvements I made after class.

[22-Sep-2012] Saturday Programming Workshop

I have reserved DMS 106 from 1pm to 3pm on Saturday in the Davidson Mathematical Sciences Building for our class. We discussed C code generation by Maple and how to pass vectors and matrices as arguments to subroutines. If you missed the workshop you may examine the files for September 22 and the improvements I made after class.

[15-Sep-2012] Saturday Programming Workshop

I have reserved DMS 106 from 1pm to 3pm on Saturday in the Davidson Mathematical Sciences Building for our class. We discussed makefiles and automatic report generation. If you missed the workshop you may examine the files for September 15.

[08-Sep-2012] Saturday Programming Workshop

I have reserved MIKC 114 from 1pm to 3pm on Saturday in the Mathewson IGT Knowledge Center for our class. We discussed how to edit and compile a C program. If you missed the workshop you may examine the files for September 8.

[07-Sep-2012] Computer Programs

The sample computer codes for our class are now available on this webpage. This mirror will be updated each night from the class server. The most up-to-date versions can always be found on the server. If you have not already done so, please log into the server to ensure you have access. Accounts that have never been logged into will be disabled in a week.

[14-Dec-2012] Final Exam

The final exam will be held on Friday, December 14 from 10:15-12:15pm in AB634.

Additional Resources

The following books contain useful information about computer programming:
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

Numerical Methods Guys, Holistic Numerical Methods.

Elementary Numerical Analysis by Prof. Rekha P. Kulkarni.

Internet Resources

Homework

Homework #1 due September 17 (solutions)
             Problems 1.3 # 11ac 14, 15, 16
    Computer Problems 1.3 # 4abc

             Problems 2.3 # 2, 5bc
    Computer Problems 2.3 # 1, 2, 5

Homework #2 due October 5 (solutions)
             Problems 3.2 # 4, 6, 17
    Computer Problems 3.2 # 1, 8, 9
             Problems 3.5 # 1, 5, 19
    Computer Problems 3.5 # 5
             Problems 3.6 # 1, 2

Homework #3 due November 23 (solutions)
             Problems 5.2 # 1, 16, 34, 39
             Problems 5.3 # 7, 11
             Problems 6.2 # 4, 25
    Computer Problems 6.2 # 1, 2

Homework #4 due December 10 (solutions)
             Problems 6.8 # 6, 8, 21
             Problems 6.9 # 2, 3, 4, 8

Grading

    2 Quizzes                 10 points each
    1 Midterm                 40 points
    4 Homework Assignments    10 points each
    2 Programming Projects    20 points each
    1 Final Exam              80 points
   ------------------------------------------
                             220 points total

Quizzes and Exams

Final Exam

The final exam will be held on Friday, December 14 from 10:15-12:15pm in AB634.

Equal Opportunity Statement

The Mathematics Department is committed to equal opportunity in education for all students, including those with documented physical disabilities or documented learning disabilities. University policy states that it is the responsibility of students with documented disabilities to contact instructors during the first week of each semester to discuss appropriate accommodations to ensure equity in grading, classroom experiences and outside assignments.

Academic Conduct

Bring your student identification to all exams. Work independently on all exams and quizzes. Behaviors inappropriate to test taking may disturb other students and will be considered cheating. Don't talk or pass notes with other students during an exam. Don't read notes or books while taking exams given in the classroom. You may work on the programming assignments in groups of two if desired. Homework may be discussed freely. If you are unclear as to what constitutes cheating, please consult with me.
Last updated: Tue Aug 21 11:53:05 PDT 2012