# CS 206: Principles of Scientific Computing Spring 2017

Instructor Xiaohui Xie ICS 180 TuTh 2:00-3:30pm DBH 4088 34710 Piazza

Course description
Overview of widely used principles and methods in scientific computing, including basic concepts and computational methods in numerical linear algebra and convex optimization. Tentative topics include
• numerical linear algebra
• QR factorization and least squares
• Conditioning and stability
• Systems of equations
• Eigenvalues
• Iterative methods
• Convex optimization
• Convex sets and convex functions
• Optimality conditions and duality
• Unconstrained optimization
• Constrained optimization
• Interior point methods
Prerequisites
multivariate calculus, linear algebra
• Grading: Based on homework (20%), a midterm (30%) and a final exam (50%).
• Homework: You may discuss each assignment with others, but are required to code and write up each assignment independently.
• Late homework policy: If you get a note from the Student's Office (personal problems) or infirmary (medical problems) requesting a postponement, it will be honored. Otherwise, late homework will not be accepted.
Lecture schedule
• Matrix-vector multiplication
• Orthogonal vectors and matrices
• Vector norms, matrix norms
• Singular value decomposition (SVD)
• QR factorization, Gram-Schmidt Orthogonalization
• Projectors, Modified Gram-Schmidt Orthogonalization
• Householder triangularization and least squares problems
• Eigenvalue problems, Rayleigh quotient, Inverse iteration, Rayleigh quotient iteration
• QR algorithm for eigenvalue problems
• Hessenberg or tridiagonal form, Computing SVD
• Convex Optimzation Problems
• Introduction
• Convex sets
Convex Sets
• Convex functions
Convex Functions
• Optimization problems, Duality
• Optimality conditions, KKT conditions
Duality
• Unconstrained optimization, gradient descent, Newton's method
Unconstrained minimization
• Constrained optimization, interior point methods
Equality constrained minimization
Interior-point methods
Homework
• Assignment #1: NLA 2.3, 2.4, 2.6, 3.2, 4.1 ** from the textbook (NLA: Numerical linear algebra)
• Assignment #2
• Assignment #3: NLA 29.1 (only sub-problems a,b,c), (due date: May 29 before class)
• Assignment #4: CO: 2.12, 3.1, 3.16, 3.17 (due date: May 30 (Tues) before class)
• Assignment #5: CO: 9.30, 10.15, 11.22 (due date: June 16 (Friday 5pm))
• The final is released on Piazza. Due date: 5pm on June 16th
Textbooks
• Numerical Linear Algebra by Trefethen and Bau - NLA
• Convex Optimization by Boyd and Vandenberghe - CO
Piazza
We will be using Piazza for class discussion. The system is highly catered to getting you help fast and efficiently from classmates and myself. Rather than emailing questions to me, I encourage you to post your questions on Piazza. If you have any problems or feedback for the developers, email team@piazza.com.

Find our class page at: https://piazza.com/uci/spring2017/cs206/home