$\newcommand{\eps}{\varepsilon} \newcommand{\kron}{\otimes} \DeclareMathOperator{\diag}{diag} \DeclareMathOperator{\trace}{trace} \DeclareMathOperator{\rank}{rank} \DeclareMathOperator*{\minimize}{minimize} \DeclareMathOperator*{\maximize}{maximize} \DeclareMathOperator{\subjectto}{subject to} \newcommand{\mat}[1]{\boldsymbol{#1}} \renewcommand{\vec}[1]{\boldsymbol{\mathrm{#1}}} \newcommand{\vecalt}[1]{\boldsymbol{#1}} \newcommand{\conj}[1]{\overline{#1}} \newcommand{\normof}[1]{\|#1\|} \newcommand{\onormof}[2]{\|#1\|_{#2}} \newcommand{\MIN}[2]{\begin{array}{ll} \minimize_{#1} & {#2} \end{array}} \newcommand{\MINone}[3]{\begin{array}{ll} \minimize_{#1} & {#2} \\ \subjectto & {#3} \end{array}} \newcommand{\MINthree}[5]{\begin{array}{ll} \minimize_{#1} & {#2} \\ \subjectto & {#3} \\ & {#4} \\ & {#5} \end{array}} \newcommand{\MAX}[2]{\begin{array}{ll} \maximize_{#1} & {#2} \end{array}} \newcommand{\MAXone}[3]{\begin{array}{ll} \maximize_{#1} & {#2} \\ \subjectto & {#3} \end{array}} \newcommand{\itr}[2]{#1^{(#2)}} \newcommand{\itn}[1]{^{(#1)}} \newcommand{\prob}{\mathbb{P}} \newcommand{\probof}[1]{\prob\left\{ #1 \right\}} \newcommand{\pmat}[1]{\begin{pmatrix} #1 \end{pmatrix}} \newcommand{\bmat}[1]{\begin{bmatrix} #1 \end{bmatrix}} \newcommand{\spmat}[1]{\left(\begin{smallmatrix} #1 \end{smallmatrix}\right)} \newcommand{\sbmat}[1]{\left[\begin{smallmatrix} #1 \end{smallmatrix}\right]} \newcommand{\RR}{\mathbb{R}} \newcommand{\CC}{\mathbb{C}} \newcommand{\eye}{\mat{I}} \newcommand{\mA}{\mat{A}} \newcommand{\mB}{\mat{B}} \newcommand{\mC}{\mat{C}} \newcommand{\mD}{\mat{D}} \newcommand{\mE}{\mat{E}} \newcommand{\mF}{\mat{F}} \newcommand{\mG}{\mat{G}} \newcommand{\mH}{\mat{H}} \newcommand{\mI}{\mat{I}} \newcommand{\mJ}{\mat{J}} \newcommand{\mK}{\mat{K}} \newcommand{\mL}{\mat{L}} \newcommand{\mM}{\mat{M}} \newcommand{\mN}{\mat{N}} \newcommand{\mO}{\mat{O}} \newcommand{\mP}{\mat{P}} \newcommand{\mQ}{\mat{Q}} \newcommand{\mR}{\mat{R}} \newcommand{\mS}{\mat{S}} \newcommand{\mT}{\mat{T}} \newcommand{\mU}{\mat{U}} \newcommand{\mV}{\mat{V}} \newcommand{\mW}{\mat{W}} \newcommand{\mX}{\mat{X}} \newcommand{\mY}{\mat{Y}} \newcommand{\mZ}{\mat{Z}} \newcommand{\mLambda}{\mat{\Lambda}} \newcommand{\mSigma}{\ensuremath{\mat{\Sigma}}} \newcommand{\mPbar}{\bar{\mP}} \newcommand{\ones}{\vec{e}} \newcommand{\va}{\vec{a}} \newcommand{\vb}{\vec{b}} \newcommand{\vc}{\vec{c}} \newcommand{\vd}{\vec{d}} \newcommand{\ve}{\vec{e}} \newcommand{\vf}{\vec{f}} \newcommand{\vg}{\vec{g}} \newcommand{\vh}{\vec{h}} \newcommand{\vi}{\vec{i}} \newcommand{\vj}{\vec{j}} \newcommand{\vk}{\vec{k}} \newcommand{\vl}{\vec{l}} \newcommand{\vm}{\vec{l}} \newcommand{\vn}{\vec{n}} \newcommand{\vo}{\vec{o}} \newcommand{\vp}{\vec{p}} \newcommand{\vq}{\vec{q}} \newcommand{\vr}{\vec{r}} \newcommand{\vs}{\vec{s}} \newcommand{\vt}{\vec{t}} \newcommand{\vu}{\vec{u}} \newcommand{\vv}{\vec{v}} \newcommand{\vw}{\vec{w}} \newcommand{\vx}{\vec{x}} \newcommand{\vy}{\vec{y}} \newcommand{\vz}{\vec{z}} \newcommand{\vpi}{\vecalt{\pi}} \newcommand{\vlambda}{\vecalt{\lambda}}$

# CS 51500 Syllabus

## Course information

Fall 2017
Tuesday and Thursdays 10:30-11:45
Forney B124
https://www.cs.purdue.edu/homes/dgleich/cs515-2017

## Instructor

David F. Gleich
Lawson 1207
dgleich@purdue.edu
https://www.cs.purdue.edu/homes/dgleich

### Office hours

Thursday from 3:30pm-4:30pm in Lawson 1207

## Teaching Assistant

Huda Nassar
hnassar@purdue.edu

### Office hours

Monday 2-3pm and Friday at 10:30-11:30am in Haas G50

## Piazza

We will use Piazza for homework questions and discussions. https://piazza.com/class/j6m8xg7h69n6p2

## Description

This course is an in-depth study of numerical linear algebra and the matrix computations that arise in solving linear systems, least squares problems, and eigenvalue problems for dense and sparse matrices. It will cover many of the fundamental algorithms such as the LU decomposition, the Cholesky decomposition, the conjugate gradient method, and the GMRES method. The course is designed for those who wish to use matrix computations in their own research.

## Prerequisites

This class is an indepth graduate lecture class. You (the student) should have taken a mathematical course on linear algebra that covers vector spaces as well as a numerical analysis course that covers computer implementations of numerical algorithms. David will assume that you have studied many of the basics of these classes.

## Goals and objectives

Matrix computations is a large area, but the basics are pretty consistent. My view is that matrix computations are effectively the standard language of mathematical computing. (Incidentally, I don't like that phrase, but I don't have a ready alternative).

When we reach the end of the class, you should be able to:

• Understand the algorithms underlying matrix computations software for dense matrices
• Be able to implement basic versions of these algorithms
• Understand the difference between iterative methods for linear systems and direct methods.
• Be able to implement iterative methods for large scale problems.
• Appreciate the variety of applications of matrix computations.

## Requirements

The formal requirements and percentage of the total course grade are:

• In-class quizzes -- 5%
• Homeworks -- 30%
• Midterm -- 32.5%
• Final -- 32.5%

There may be extra-credit opportunities throughout the class. Finally, you must meaningfully participate in each of the three components (homeworks, midterm, and final). Lack of participation in one area may result in a failing grade for the class or a multiple letter grade reduction. (That is, someone who gets a 65% average on the exams and doesn't do any homework might be able to get a D; this policy would reduce their grade to an F; someone who aced both homeworks and the midterm but skipped the final could have gotten a B-, this would reduce them to a C or D. )

### Quizzes

These will be worth 5% of the total grade and are graded as taken/missed. Students can miss up to 5 quizzes with no penalty. Make sure you contact the instructor (David) if you anticipate missing more than 5 quizzes due to any absenses as there may be some accomodation in special circumstances. Note that this is an all-or-nothing grade.

### Quizzes for distance students

Distance students are required to submit "magic numbers" announced in class to blackboard in-lieu of submitting the in-class quiz. Again, students can miss up to 5 of these scores with no penalty. Distance students will have up to 48 hours from the start of the lecture to to submit their quiz on blackboard before it is marked "missed".

## References

The required/recommended text book is:

Matrix Computations. Gene H. Golub and Charles van Loan. 4th Edition, Johns Hopkins University Press.

Numerical Linear Algebra. Lloyd N. Trefethen and David Bau. SIAM

There are other books that may be useful:

• James Demmel, Applied numerical linear algebra, SIAM 1997
• Yousef Saad, Iterative Methods for Sparse Linear Systems Second Edition
• See a longer list at the references page.

## Policies

### Conduct and Courtesy

Students are expected to maintain a professional and respectful classroom environment. In particular, this includes:

• silencing personal electronics
• arriving on time and remaining throughout the class
• do not insult or deride others for any reason (even in jest)
• be on time for class
• please leave class promptly and wait to ask me questions in the hall, unless they pertain to material on the blackboard.

You may use any non-disruptive personal electronics during class. One exception is during in-class quizzes and tests, for which personal electronics are prohibited.

### Announcements

There will be announcements relevant to the course made through the ITaP course email list. This will send an email message to your purdue email address and you are expected to check this account for information related to the class. We will verify that everyone in the class is receiving these messages early on.

### Correspondence

The best way to correspond in this class is to post a note on Piazza.

Please feel free to email me with any questions, but please prefix all email titles with the string CS-51500 MC: to aid in filtering email. Also, consider using a private note on Piazza instead.

I will make every effort to respond promptly, however, replies could be delayed due to circumstances outside of my control. In particular, do not rely on a response between the hours of 8pm and 8am.

Please do not attempt to call, google chat, skype, facebook, or tweet with me without prior arrangement.

### Assignment clarity

I expect all assignments to be legible and well-written.
Mathematical derivations alone are insufficient and you must explain your reasoning in sentences. For this, I require using a computer to prepare all submitted materials.

If you cannot use a computer and LaTeX to prepare solutions to homeworks, I am willing to consider exceptions to this policy.

Also, using LaTeX can increase the temptation to share answers. All LaTeX must be written individually.

### Missing or late work

Except as discussed below, and or by prior arrangement, missing or late work will be counted as a zero.

### Collaboration

Collaboration on homework is allowed. The final assignments must contain a list of all collaborators. However, students must prepare solutions individually. As an example of the ideal scenario, the following situation is permissible:

A group of students meets to develop the solution to a problem on a white board. Each student records individual notes from this problem solving meeting. All students then prepare solutions individually and without further collaboration. These solutions list the names of all members in the initial group.

The final assignments must contain a list of all collaborators, regardless of if they are in the class or not. Failure to list collaborators will result in a zero on any homework, you must write I did not collaborate with anyone on this homework'' if you worked on the homework entirely alone.

Examples of collaborations that are not allowed include, but are not limited to:

• Sharing pieces of any written solution
• Sharing source code or any other computer programs
• Reviewing final written solutions

### Computer codes

The assignments will involve producing computer codes. These need to be documented and written in accordance with best software engineering practices. Failure to follow this advice may result in solutions receiving zero points. Moreover, these should be prepared individually. Groups may discuss implementation strategies, algorithms, and approaches; but codes, like written homework solutions, must be prepared separately.

Debugging

What to do about debugging? That's right, you've gotten the ideas down. You think you have the algorithm right, you coded it. And yet, it still doesn't work. But you can't ask a friend because you can't share code, right? Here is what you should do. Spend 30 minutes working with that code to try and make it work. Write down what you did. If, after that, it still doesn't work. Then spend 15 minutes explaining what your problem is to a friend without looking at the code.

• A -- 85-100%
• B -- 65-85%
• C -- 50-65%
• D -- 40-50%
• F -- 0-40%

These may be adjusted downward by up to 10% to achieve a reasonable grade distribution. They also may be minor upward adjustments.

Behavior consistent with cheating, copying, and academic dishonesty is not tolerated. Depending on the severity, this may result in a zero score on the assignment or exam, and could result in a failing grade for the class.

Purdue prohibits "dishonesty in connection with any University activity. Cheating, plagiarism, or knowingly furnishing false information to the University are examples of dishonesty." (Part 5, Section III-B-2-a, University Regulations) Furthermore, the University Senate has stipulated that "the commitment of acts of cheating, lying, and deceit in any of their diverse forms (such as the use of substitutes for taking examinations, the use of illegal cribs, plagiarism, and copying during examinations) is dishonest and must not be tolerated. Moreover, knowingly to aid and abet, directly or indirectly, other parties in committing dishonest acts is in itself dishonest." (University Senate Document 72-18, December 15, 1972)

You are expected to read both Purdue's guide to academic integrety and Prof. Gene's Spafford's guide as well. You are responsible for understanding their contents and how it applies to this class.

### Attendance

Students are expected to be present for every meeting of the classes in which they are enrolled. Only the instructor can excuse a student from a course requirement or responsibility. When conflicts or absences can be anticipated, such as for many University sponsored activities and religious observations, the student should inform the instructor of the situation as far in advance as possible. For unanticipated or emergency absences when advance notification to an instructor is not possible, the student should contact the instructor as soon as possible by email, or by contacting the main office that offers the course. When the student is unable to make direct contact with the instructor and is unable to leave word with the instructor's department because of circumstances beyond the student's control, and in cases of bereavement, the student or the student's representative should contact the Office of the Dean of Students.

### Grief Absence Policy

Purdue University recognizes that a time of bereavement is very difficult for a student. The University therefore provides the following rights to students facing the loss of a family member through the Grief Absence Policy for Students (GAPS). GAPS Policy: Students will be excused for funeral leave and given the opportunity to earn equivalent credit and to demonstrate evidence of meeting the learning outcomes for misses assignments or assessments in the event of the death of a member of the student's family.

### Violent Behavior Policy

Purdue University is committed to providing a safe and secure campus environment for members of the university community. Purdue strives to create an educational environment for students and a work environment for employees that promote educational and career goals. Violent Behavior impedes such goals. Therefore, Violent Behavior is prohibited in or on any University Facility or while participating in any university activity.

### Students with Disabilities

Purdue University is required to respond to the needs of the students with disabilities as outlined in both the Rehabilitation Act of 1973 and the Americans with Disabilities Act of 1990 through the provision of auxiliary aids and services that allow a student with a disability to fully access and participate in the programs, services, and activities at Purdue University. If you have a disability that requires special academic accommodation, please make an appointment to speak with me within the first three (3) weeks of the semester in order to discuss any adjustments. It is important that we talk about this at the beginning of the semester. It is the student's responsibility to notify the Disability Resource Center (http://www.purdue.edu/drc) of an impairment/condition that may require accommodations and/or classroom modifications.

### Emergencies

In the event of a major campus emergency, course requirements, deadlines and grading percentages are subject to changes that may be necessitated by a revised semester calendar or other circumstances beyond the instructorâ€™s control. Relevant changes to this course will be posted onto the course website or can be obtained by contacting the instructors or TAs via email. You are expected to read your @purdue.edu email on a frequent basis.

### Emergency Preparedness

Emergency notification procedures are based on a simple concept:

if you hear a alarm inside, proceed outside.
if you hear a siren outside, proceed inside.

Indoor Fire Alarms are mean to stop class or research and immediately evacuate the building. Proceed to your Emergency Assembly Area away from building doors. Remain outside until police, fire, or other emergency response personnel provide additional guidance or tell you it is safe to leave.

All Hazards Outdoor Emergency Warning sirens mean to immediately seek shelter (Shelter in Place) in a safe location within the closest building. "Shelter in place" means seeking immediate shelter inside a building or University residence. This course of action may need to be taken during a tornado, a civil disturbance including a shooting or release of hazardous materials in the outside air. Once safely inside, find out more details about the emergency. Remain in place until police, fire, or other emergency response personnel provide additional guidance or tell you it is safe to leave.

### Nondiscrimination

Purdue University is committed to maintaining a community which recognizes and values the inherent worth and dignity of every person; fosters tolerance, sensitivity, understanding, and mutual respect among its members; and encourages each individual to strive to reach his or her own potential. In pursuit of its goal of academic excellence, the University seeks to develop and nurture diversity. The University believes that diversity among its many members strengthens the institution, stimulates creativity, promotes the exchange of ideas, and enriches campus life.

Purdue University prohibits discrimination against any member of the University community on the basis of race, religion, color, sex, age, national origin or ancestry, marital status, parental status, sexual orientation, disability, or status as a veteran. The University will conduct its programs, services and activities consistent with applicable federal, state and local laws, regulations and orders and in conformance with the procedures and limitations as set forth in Executive Memorandum No. D-1, which provides specific contractual rights and remedies.

## Schedule

A tentative list of lectures is on the schedule page for a list of lecture topics. This list will not evolve throughout the course. See the web-page for an up-to-date list of lectures, see the readings page

See the schedule page for a list of lecture topics

### Instructor absence

David (your instructor) has a few planned absenses this term. We will hold class as usual with another instructor, your TA, or a video lecture.

### Makeup classes

If we need to reschedule additional classes, we will do so on an as-needed basis. Our plan is to use video lectures to supplement for any missing class periods.

## Changes

This syllabus is subject to change. Updates will be posted on the course website and announced via email.

• Initial version: 2017-08-21
• Updates with distance student quizzes and office hours: 2017-08-31