CAAM 454 / 554 · Numerical Analysis IISpring 2018 · Rice University

ABOUT THIS COURSE: 
Iterative methods for linear systems of equations including Krylov subspace methods; Newton and Newtonlike methods for nonlinear systems of equations; Gradient and Newtonlike methods for unconstrained optimization and nonlinear least squares prob lems; techniques for improving the global convergence of these algorithms; linear program ming duality and primaldual interiorpoint methods. 
LECTURES: 
Tues/Thurs 2:30pm3:45pm, Duncan Hall 1046 
INSTRUCTOR: 
Matthias Heinkenschloss (heinken_AT_rice.edu),
Duncan Hall 3088, (713) 3485176 Office hours: M+F 12pm. 
454 or 554? 
Students may take this course as either CAAM 454 or 554: both meet for the same T/Th lectures, but CAAM 554 will include more theoretical homework and exam problems, and potentially some supplemental lectures with additional theoretical material. CAAM graduate students must enroll in CAAM 554; others comfortable writing rigorous mathematical proofs may also consider this option. Students cannot take both CAAM 454 and 554 for credit. 
PROBLEM SETS: 
Problem sets will be assigned roughly once a week.
There will be two pledged problem sets/ exams. On unpledged assignments you may collaborate, but your writeup must be your own independent work. Exams/pledged homework assignments may be timed and `closed book', and you are not allowed to discuss exams/ pledged assignments with anyone but your instructor. Transcribed solutions are unacceptable; you may not consult solutions from previous sections of this class. 
GRADING: 
60% unpledged problem sets, 40% pledged (Class participation, improving performance on the pledged homeworks, and feedback on the handouts will be considered when assigning borderline grades.) 
LATE POLICY: 
You may turn in two unpledged problem sets one class period late without penalty. Subsequent late assignments will be penalized 20% each. Homework will not be accepted more than one class period late without a written excuse. This implies that you may not use two `lates' on one assignment. Pledged assignments/exams must be turned in on time. 
COURSE NOTES: 
Course notes will be posted on CANVAS. The lectures page contains required and additional reading for the lectures. 
SYLLABUS: 

RECOMMENDED 
J. E. Dennis, Jr., and R. B. Schnabel, Numerical Methods for Unconstrained
Optimization and Nonlinear Equations, SIAM, 1996. C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations, SIAM, 1995. C. T. Kelley, Iterative Methods for Optimization, SIAM, 1999. J. Nocedal and S. J. Wright, Numerical Optimization(second edition), Springer Verlag, 2006. Y. Saad, Iterative methods for sparse linear systems(2nd edition)}, SIAM, 2003. L. N. Trefethen and D. Bau, III, Numerical Linear Algebra, SIAM, 1997. 
http://www.caam.rice.edu/~caam454 http://www.caam.rice.edu/~caam554