ECS130, Winter 2021
Scientific Computation (Numerical Algorithms)

Instructor

Zhaojun Bai,
Office: 3005 Kemper Hall
Phone: 752-4874
Email: bai at cs.ucdavis.edu

Teaching Assistant

TBA

Lecture

TR 10:30am -- 11:50am Olson 250

Discussions

T 12:10pm - 1:00pm Cruess 1003

Office Hours

W.R.: 1:30pm -- 3:00pm, Room 3005 Kemper (Prof. Bai)
OH by TA (TBA)

Textbook:

Numerical Algorithms: methods for computer vision, machine learning, and graphics
by Justin Solomon, CRC Press, 2015

Software:

• MATLAB
  • Numerical Computing with MATLAB (revised reprint) by C. Moler, SIAM, 2008
    Electronic Edition
    
  • MATLAB for Student
  • Interactive MATLAB Tutorial
  • New: 2-hour MATLAB onramp
• Julia
  • The Julia programming language

Course Objectives:

• From biological modeling, to physical simulation, to graphics and image (data) processing, to data mining and social network analysis, the need for accurate and fast numerical algorithms is expanding. With problems of very large size and under the limitations of finite precision arithmetic, the design of practical algorithms becomes a challenging task. Numerical algorithms (scientific computation) is the broad field concerned with the design and analysis of efficient numerical algorithms. In this course, we will learn basic ideas and fundamental numerical algorithms in scientific computing. You can ``play'' with the mathematics that stands behind each and every new method that you learn, use graphics to appreciate convergence and error, use matrix-vector programming language to solidify the understanding of linear algebra and to prepare for advanced array-level computing.

Topics:

1. Mathematics review
2. Numerics and error analysis
3. Linear algebra: linear systems, eigenvalues and eigenvectors, singular value decomposition
4. Nonlinear techniques: nonlinear systems, optimization
5. Function approximations, derivatives and integrals.

Grading breakdown:

• Homework: 50%
• Exam/Project: 50%
• Homework box is located in Room 2131, Kemper Hall

Online Info:

• Annoucements, handouts and homework assignments will be posted at this course site. It gets updated frequently throughout the quarter.
• canvas site

Lecture-by-lecture summaries and assignments

Date	Topics	Reading	Homework
1/7	Mathematics review (1/2)	Secs.1.1 -- 1.3
1/9	Mathematics review (2/2)	Slides	1.2, 1.3, 1.4, 1.7, 1.12, 1.15, 1.16 (page 23)
1/11	Linear systems and LU (1/2)	Chapter 3 Slides, notes	Homework 1
1/14	Linear systems and LU (2/2)	Handout	Matlab codes lutx.m, bslashtx0.m
1/16	Designing linear systems	Secs.4.1.1, 4.1.2, 4.1.3	...
1/18	SPD and Cholesky	Sec.4.2.1, notes	Homework 2
1/21	Martin Luther King Jr. Holiday	...	...
1/23	Analyzing linear systems (1/2)	Sec.4.3	...
1/25	Analyzing linear systems (2/2)	notes	...
1/28	Column spaces and QR (1/2)	Chap. 5	...
1/30	Column spaces and QR (2/2)	notes	Homework 3
2/1	Eigenvectors (1/4)	Sec.6.2, Slides, Handout	...
2/4	Eigenvectors (2/4)	Sec.6.2 and Sec.6.3. Slides, Handout	Extra reading: List item #1
2/6	Eigenvectors (3/4) Review for midterm	Sec.6.3	Homework 3 due
2/8	Midterm I	...	Homeworks 1-3
2/11	Eigenvectors (4/4)	Sec.6.4	Homework 4
2/13	SVD (1/2)	Chap. 7, Handout	svdpcaeg1.m, svdpcaeg2.m, svd4image.m Extra reading: List item #2
2/15	SVD (2/2)	...	Extra reading: List item #3
2/18	President's Day Holiday	...	...
2/20	Nonlinear systems 1/2	Sec. 8.1	Homework 5
2/22	Nonlinear systems 2/2	Sec.8.2.1	zeroseg1.m, zeroseg2.m, zeroseg3.m, zeroseg4.m, fzerotx.m, call fzerotx
2/25	Unconstrained optimization 1/2	Secs. 9.1, 9.2, 9.3.1, 9.4.1	...
2/27	Unconstrained optimization 2/2	Slides	lsbygd2.m, data2D.mat Homework 6, due 4pm, Mar.8
3/1	no class, make up at the final week	...	...
3/4	Interpolation 1/2	Sec.13.1 Slides	interpeg1.m, interpeg2.m, interpeg3.m polyinterppower.m polyinterp.m,
3/6	Interpolation 2/2	...	interpeg4.m piecelin.m
3/8	Integration and differentiation 1/2	Chap. 14 Slides	Homework 6 due quadeg1.m, quadeg2.m quadeg3.m, quadtx.m
3/11	Midterm II	...	Homeworks 4, 5, 6
3/13	Integration and differentiation 2/2	outline	diffeg1.m, diffeg2.m
3/15	Essential ideas of ``deep learning'' (Instruction ends)	Slides	Additional reading: List item #4
3/18	Office hours 1:30pm - 3:00pm, 47 Kemper Office hours 4:00pm - 5:30pm, 3005 Kemper	...	...
3/19	Office hours 1:30pm - 3:00pm, 47 Kemper	...	...
3/20	Office hours 1:30pm - 3:00pm, 3005 Kemper	...	...
3/21	3:00pm, Final project report due	...	Final project assignment mnistdata.mat (13MB), viewdigit.m Related reading material Project report guideline