MATH 8664-001 ITERATIVE METHODS IN NUMERICAL LINEAR ALGEBRA

Spring 2010. University of Colorado Denver

MATH 8664-3. Iterative Methods in Numerical Linear Algebra. Every other year.
Preconditioned iterative methods for linear systems and eigen problems, conjugate gradients, multigrid and domain decomposition.
Prereq: MATH 5660 and MATH 7665.

Meetings CU-Dravo 641. T R - 11:30AM to 12:45PM

INSTRUCTOR:
Prof. Andrew Knyazev
Office: CU (Dravo) 644. Phone: 303 556-8102.
Office hours: by appointment
WWW: http://math.ucdenver.edu/~aknyazev/

TEXTBOOKS:


Iterative Methods for Solving Linear Systems, Anne Greenbaum
Format: Paperback, 220pp. ISBN: 089871396X Publisher: Society for Industrial & Applied Mathematics Pub. Date: September 1997
$50 for SIAM members, $70 from amazon.com (prices may change without notice).

Please note that the SIAM offers 30% off list price discounts on books to SIAM members and at present every graduate student at the UC Denver can get a FREE SIAM membership! Read about Complimentary Graduate Student Memberships and join SIAM today!

SUBJECT:
The course will cover basic aspects of iterative methods and preconditioning for linear systems and symmetric eigenvalue problems.

This is the highest-level graduate class. It will require an independent work and a significant intellectual effort in particular, to learn PETSc and Hypre software packages and basics of parallel programming, though, help will be provided. Computer projects will be PETSc and Hypre based programming assignments as well as theoretical.

It is expected that students solve most of the problems of the textbook, suggested as exercises after every section, as their homework, but solutions will not be collected. Hard problems will be discussed in class.

GRADING will based on Individual Projects:

Software projects:

CONTENTS: The class will be based on research articles and the textbook. From the textbook, the class will touch the following major topics in a depth that will be determined by the pace of the class.

Chapter 1. Introduction

Part I. Krylov Subspace Approximations

Chapter 2. Some Iteration Methods

Chapter 3. Error Bounds for CG, MINRES, and GMRES Chapter 4. Effects of Finite Precision Arithmetic Chapter 5. BiCG and Related Methods Chapter 6. Is There a Short Recurrence for a Near-Optimal Approximation? Chapter 7. Miscellaneous Issues Part II. Preconditioners

Chapter 8. Overview and Preconditioned Algorithms

Chapter 9. Two Example Problems

Chapter 11. Incomplete Decomposition Chapter 12. Multigrid and Domain Decompositon Methods If time allows, a short review of preconditioned eigensolvers will be presented using
Templates for the Solution of Algebraic Eigenvalue Problems: a Practical Guide, Section Preconditioned Eigensolvers by A. Knyazev.


Spring 2010 Semester -- Key Dates

JANUARY 19, 2010: First day of Class

JANUARY 24, 2010:

  • Last day to be added to a wait list using the SMART system.

  • Last day to add a course using the SMART system.

  • JANUARY 25, 2010:

  • LAST DAY TO DROP WITHOUT DROP CHARGE – THIS INCLUDES SECTION CHANGES. NO ADDS PERMITTED TODAY.

  • Wait Lists are dropped.  Any student who was not added to a course automatically from the wait list by this date and time MUST complete a drop/add form to be added to the class.  Students are NOT automatically added to the class from the wait list after this date and time.  If your name is not on the official student roster, you are not registered for the course.

  • JANUARY 26, 2010: First day instructor may approve request to add a student to a full course using a Schedule Adjustment Form. Independent study, internship, thesis and dissertation credit, and candidate for degree may be added with required signature approvals using a Special Processing Form.

    JANUARY 26-February 3, 2010: Students are responsible for verifying an accurate spring 2010 course schedule via the SMART registration system.  Students are NOT notified of their wait-list status by the university.  All students must check their scheduled prior to February 3, 2010 for accuracy.

    FEBRUARY 3, 2010 at 5 PM:

  • Last day to add structured courses without a written petition for a late add.  This is an absolute deadline and is treated as such. This deadline does not apply to independent study, internships, project hours, thesis hours, dissertation hours, and late-starting modular courses.

  • Last day to drop a spring 2010 course with a tuition adjustment minus the drop charge and no transcript notation – this includes section changes.  Drops after this date will appear on your transcript.  This is an absolute deadline and is treated as such.

  • Last day to completely withdraw from all spring 2010 courses with a tuition adjustment and no transcript notation. Drop charge applies. Drops after this date will appear on your transcript.  This is an absolute deadline and is treated as such.






  • FEBRUARY 15-24, 2010: Faculty can use the early alert system.

    MARCH 22-28, 2010: Spring Break.

    APRIL 2, 2010 at 5 PM: Last day for non CLAS students to drop or withdraw from all classes without a petition and special approval from the student’s academic Dean.  This is treated as an absolute deadline.

    APRIL 16, 2010 at 5 PM: Last day for CLAS students to drop or withdraw from all classes without a petition and special approval from the student’s academic Dean. Students still need signatures from the faculty and Dean.  This is treated as an absolute deadline.
    After April 16, 2010 all schedule changes require a petition.  Petitions are available in NC 4011.

    No schedule changes will be granted once finals week has started.  There are NO exceptions to this policy.

    May 10-15, 2010: Finals Week.

    May 15, 2010: Last day of spring semester.

    May 15, 2010: Commencement:  Auraria Playing Fields, 9 a.m.

    May 26, 2010: Spring final grades available on S.M.A.R.T.


    CLAS Incomplete (IW/IF) Policy

    The faculty in the College of Liberal Arts and Sciences passed the following policy relating to the awarding of incomplete grades.  This CLAS policy is consistent with the UC Denver campus policy.

    Incomplete grades (IW or IF) are NOT granted for low academic performance.  To be eligible for an Incomplete grade, students MUST:

    1. Successfully complete a minimum of 75% of the course
    2. Have special circumstances beyond their control that preclude them from attending class and completing graded assignments
    3. Make arrangements to complete missing assignments with the original instructor. Verification of special circumstances is required.  

    Completion of a CLAS Course Completion Agreement is strongly suggested. Incompletes cannot be awarded that stipulate: (1) a student may repeat the entire course, (2) repeat or replace existing grades, (3) allow the student an indeterminate period of time to complete a course, or (4) allow the student to repeat the course with a different instructor.

    The CLAS Course Completion Agreement is available from the CLAS Advising Office, NC 4002.


    Disability Accommodations

    The faculty at the University of Colorado system have both a legal and moral obligation to provide reasonable accommodations to students with disabilities.  To be eligible for accommodations, students must be registered with the UC Denver Office of Disability Resources and Services (DRS) -- North Classroom 2514; 303-556-3450, 303-556-4766 TDD).  The DRS staff has experience to assist faculty in determining reasonable accommodations and to coordinate these accommodations.  If a student is given accommodations, they must be followed.  If a student chooses not to accept the accommodations set forth by the DRS, they MUST complete all assignments and do all course work in the same manner as all other students.  No exceptions or alternate forms of evaluation can be used except those mandated by the DRS.  Faculty cannot arbitrarily decide to give a student extra time, extra assistance or other forms of aid unless it is formally mandated by the DRS.


    Required course syllabus information from UC Denver and CLAS: