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- Common Cource of Engineering

- School of Bioscience and Biotechnology
- Common Course of Undergraduate School

- Graduate School of Science and Engineering
- Mathematics
- Physics(Particle- Nuclear- and Astro-Physics)
- Physics(Condensed Matter Physics)
- Chemistry
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- Mechanical Sciences and Engineering
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- Electrical and Electronic Engineering
- Physical Electronics
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- Graduate School of Information Science and Engineering
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- Common Course of Graduate School
- Program for Leading Graduate Schools

- Lecturer
- Kim Sunyoung

- Place
- Tue3-4(W832) Tue7-8(W832)

- Credits
- Lecture2 Exercise0 Experiment0

- Code
- 75006

- Syllabus updated
- 2014/10/3

- Lecture notes updated
- 2014/9/18

- Semester
- Fall Semester

Numerical linear algebra and conic optimization

We will give a brief introduction to the basic ideas of numerical linear

algebra and conic optimization. The rst part of this course will cover topics from

numerical linear algebra that are necessary for the implementation of optimization

methods. Numerical solutions of linear systems, matrix factorizations, and least

squares methods will be discussed from the theoretical and algorithmic aspects. The

second part of the course will be devoted to the optimization methods, focusing on

conic programming. In particular, semidenite programming and recent advances

in completely positive programming will be discussed.

Lecture 1 What is Numerical Linear Algebra? linear algebra-historical notes,

one application

Lecture 2 Notation, basic concepts in Numerical Linear Algebra,

range, null space, matrix and vector norms

Lecture 2-3 Linear Equations: Gaussian elimination, pivoting

Lecture 4 Positive denite systems,

Sparse systems, banded systems

Lecture 5-6 Orthogonalization and Least squares problems

Singular value decomposition, QR factorization, Householder orthogonalization

Lecture 7-8 Nearly rank decient system

Givens rotation

Lecture 9-10 Semidenite programming: theory and applications

Lecture 11-12 Semidenite programming: theory and applications

Lecture 13-14 Semidenite programming: theory and applications

Lecture 15 Comptely positive programming, doubly nonnegative programming

Lecture 16 Exam

An Introduction to Numerical Analysis by Endre Suli and

David Mayers, Cambridge, 2003.

Numerical Linear Algebra by Lloyd N. Trefethen and David Bau, III, SIAM, 1997.

Convex Optimization by Stephen P. Boyd, Cambridge, 2004.

Background in linear algebra and Matlab programming.

One closed book exam