Mathematics 580: Introduction to Numerical Analysis I
Fall term, 2016, 9:10-10:00 MWF, Withers 125

Instructor: C. T. Kelley

This is the home page for MA 580. Most of the data here will also be on the course Moodle page. If you are not an NCSU student, then Moodle means nothing to you. Enjoy the lectures and the video recordings.

• Part I : Management and course policies. Lecture 1.
• Part II : Notation, important matrices, errors, stability, conditioning. Lectures 2 - 4
• Part III : Introduction to linear equations, Banach Lemma.
• Part IVa: Gaussian Elimination, general matrices, pivoting, errors.
• Part IVb: Gaussian Elimination, problems with special structure.
• Part Va: Linear Least Squares, normal equations, QR decomposition.
• Part Vb: Linear Least Squares, Singular Value Decomposition.
• Part VIa: Stationary Iterative Methods for Linear Equations.
• Part VIb: Krylov methods intro; GMRES theory and implementation.
• Part VIc: GMRES Examples.
• Part VId: Conjugate Gradient Iteration. Lectues
• Part VIIa: Nonlinear Equations, Picard iteration, Newton's method.
• Part VIIb: Newton-Krylov Methods, Global Convergence.
• Part VIIc: Nonlinear Least Squares.
• Part VIIIa: Eigenvalue Problems, Power Method, Rayleigh Quotient iteration.
• Part VIIIb: Eigenvalue conditioning.
• Part IXa: Residual Correction.
• Part IXb: Multigrid.

Files:

• Software examples
• KL and KNL solvers
• Nonlinear Solvers from my 2003 Newton's Method book.
• Linear and Nonlinear solvers from my 1995 Linear and Nonlinear equations book.
• KL Examples

Books: All are e-books free to NCSU students.
Other people can get the books from SIAM .

• Numerical Matrix Analysis, I. C. F. Ipsen, SIAM 2009.
• Iterative Methods for Linear and Nonlinear Equations, C. T. Kelley, SIAM 1995.
• Matlab Guide: Second Edition, Desmond J. Higham and Nicholas J. Higham, SIAM 2005.

Rules: Everything you need to know is in Part I of the lecture notes, except the summary of the late homework policy .

• NCSU Fall Calendar
• August 17, Classes begin.
• August 29 , In class exam #1. sample questions for exam #1
• September 5, Labor Day.
• October 3 , Mid-term exam #2.
• October 6-7, Fall Break.
• November 18 , Mid-term exam #3.
• November 23-25, Thanksgiving holiday.
• December 2, Last day of classes
• Wednesday, December 14, 8AM: Final exam for MA 580

• The NETLIB collection.
• Tim's new nonlinear solver codes.
• Tim's old iterative linear/nonlinear solver codes.
• Tim's latest alpha-test linear/nonlinear solver codes

HELP

• A very useful book about numerical methods by the inventor of MATLAB.
• A really useful page from the University of Houston. This one covers Matlab and LaTeX.
• UCLA MATLAB online Reference Document ,
• MATLAB help from Indiana,
• EOS/Unity Guide
• sample.tex

Students will receive an email message directing them to a website where they can login using their Unity ID and complete evaluations. All evaluations are confidential; instructors will not know how any one student responded to any question, and students will not know the ratings for any instructors.

Evaluation website: https://classeval.ncsu.edu/
Student help desk: classeval@ncsu.edu
More information about ClassEval: https://www.ncsu.edu/UPA/classeval/