M393D / CAM393D Iterative Methods and Fast Algorithms

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Course information:

• Instructor: Lexing Ying, lexing@math.utexas.edu, 471-3149, RLM 10.164
  
• Lecture: TTh 12:30-2pm, RLM 11.176
• Office hour: TTh 2-3pm.
  
• Webpage: http://www.math.utexas.edu/users/lexing/courses/Spring2009_M393D/index.html
  

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Course description:

This course contains two parts. The first part is about iterative methods for solving linear and nonlinear equations. We will cover the following topics: classical iterative methods, Krylov subspace iterative methods, preconditioners, multigrid, domain decomposition, basic convex optimization, and adjoint method.

In the second part, we will focus on the study of fast algorithms for applying structured linear operators. Topics in this part include fast Fourier transform, nonuniform fast Fourier transform, fast multipole method, directional multilevel algorithm, butterfly algorithm, and random projection method.

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Textbook:

Required:

• Iterative methods for sparse linear systems by Yousef Saad (2nd edition). The first edition can be found at the author's website.

Other references:

• Matrix computation by Golub and Van Loan
  
• A first course in the numerical analysis of differential equations by Iserles
• A multigrid tutorial by Briggs et al.
• Domain decomposition: parallel multilevel methods for elliptic partial differential equations by Smith et al.
• Convex optimization by Boyd and Vandenberghe (electronic copy available from the book website)
  
• Numerical optimization by Nocedal and Wright (electronic copy available from library website)

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Prerequisite and degree relevance:

• Linear algebra. Some knowlege about programming in Matlab, C or Fortran.

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Grading:

• Mostly based on attendance and homework.

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Homeworks:

• hw01.pdf
• hw02.pdf
• hw03.pdf

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Notes:

• lec01.pdf
• lec02.pdf
• lec03.pdf
• lec04.pdf
• lec05.pdf
• lec06.pdf
• lec07.pdf
• lec08.pdf
• lec09.pdf
• lec10.pdf
• lec11.pdf
• lec12.pdf
• lec13.pdf

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Disabilities:

The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.

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Policy on scholastic dishonesty:

Students who violate university rules on scholastic dishonesty are subject to disciplinary penalties, including the possibility of failing in the course and/or dismissal from the University. Since such dishonesty harms the individual, all students, and the integrity of the University, policies on scholastic dishonesty will be strictly enforced. For further infomation, please visit the Student Judicial Services web site at http://deanofstudents.utexas.edu/.   

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