DATE TOPIC and ASSIGNMENT READING
ARITHMETIC, CONDITIONING, and STABILITY
==WEEK 1== ======= 26 AUG Course Introduction. 28 AUG Condition Numbers [D] 1.1-1.5 IEEE floating point arithmetic 28 AUG ==WEEK 2== ======= 4 SEP 6 SEP Effects of floating point arithmetic [D] 1.6 ==WEEK 3== ======= 9 SEP Vector and Matrix Norms [D] 1.7
SOLVING LINEAR EQUATIONS
11 SEP Perturbation Theory [D] 2.1-2.2 13 SEP Gaussian Elimination [D] 2.3 First Problem Set Due: Question 1.10, Question 1.16 (Parts 6 and 7), Question 2.3. Solutions: [Postscript] [Acrobat] ==WEEK 4== 16 SEP Error Analysis [D] 2.4 18 SEP Iterative Refinement [D] 2.5 20 SEP ==WEEK 5== ======= 23 SEP Special Linear Systems [D] 2.7
LINEAR LEAST SQUARES PROBLEMS
25 SEP [D] 3.1 "Number of the Beast" demonstration: [PostScript] [Acrobat] 27 SEP Normal Equations [D] 3.2.1, 2.7.1
DATE TOPIC and ASSIGNMENT READING
==WEEK 6== ===== 30 SEP QR Factorization [D] 3.4 2 OCT 4 OCT
EIGENVALUE PROBLEMS
==WEEK 7== 7 OCT Schur canonical form [D] 4.2 Second Problem Set Due: [Postscript] [Acrobat] Solutions: [Postscript] [Acrobat] 9 OCT FIRST MIDTERM EXAM 11 OCT Perturbation theory [D] 4.3 ==WEEK 8== ======= 14 OCT Power method, Inverse iteration [D] 4.4.1-2 16 OCT Orthogonal iteration, QR iteration [D] 4.4.3-8 18 OCT Symmetric matrices [D] 5.2-3
NONLINEAR SYSTEMS OF EQUATIONS
==WEEK 9== ======= 21 OCT Nonlinear Problems in one variable [DS] Chapter 2 23 OCT NO CLASS MEETING Prepare §2.8 #1 and #7 for class Friday. 25 OCT ==WEEK 10== 28 OCT Multivariable Calculus Background [DS] Chapter 4
NEWTON'S METHOD for NONLINEAR EQUATIONS and OPTIMIZATION
30 OCT Newton's method for systems [DS] §§5.1-2 of nonlinear equations Local convergence of Newton's method. 1 NOV Kantorovich Theorem, Contractive Mapping [DS] §5.3 ====================================================================== DATE TOPIC and ASSIGNMENT READING ====================================================================== ==WEEK 11== 4 NOV Finite-Difference Derivatives [DS] §5.4 Third Problem Set Due: [Postscript] [Acrobat] Solutions: [Postscript] [Acrobat] 6 NOV Second Midterm Exam
Global Convergence of Newton's Method
8 NOV Descent directions [DS] §6.1-2 ==WEEK 12== 11 NOV Line search [DS] §6.3 13 NOV Trust region methods [DS] §6.4 15 NOV Global methods for nonlinear equations [DS] §6.5 ==WEEK 13==
STOPPING, SCALING and TESTING
18 NOV [DS] §§7.1-3
SECANT METHODS for NONLINEAR EQUATIONS
20 NOV Broyden's method [DS] §8.1 22 NOV Quasi-Newton methods [DS] §8.2-3
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[ 25-29 NOV ==== THANKSGIVING BREAK ============ ]
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Fri 29 
BUY NOTHING DAY
SECANT METHODS FOR OPTIMIZATION
==WEEK 14== 2 DEC 4 DEC 6 DEC Fourth Problem Set Due: [Postscript] [Acrobat] Solutions: [Postscript] [Acrobat] ==WEEK 15== ======== 9 DEC 11 DEC 13 DEC ==Final Exams================== 16-20 DEC 18 DEC Take-Home Final Exam [PostScript] [Acrobat] Due, 12:00 Noon. =========================THE=END=============================================
