Rensselaer Polytechnic Institute MATH 6590, Spring 2024

This is the official website for course Math 6590: Randomized Numerical Linear Algebra in Spring 2024.

This website contains most of the information you need for this course (lecture notes, assignments). Course sensitive information (announcements, exam, grade distribution etc.) will be posted on LMS (Rensselaer credentials required).

General information

Please read the course syllabus VERY CAREFULLY

Instructor: Fabian M. Faulstich

Lecture: TueFri 10:00AM - 12:00AM Carnegie 206

Office hours: Tue 1:00PM-2:00PM, Thu 4:00PM-5PM. 406 Amos Eaton Hall

Piazza page: General questions about the course and its content, which might be of interest to other students, can be asked on the piazza page.

Gradescope page: Homework assignments are to be submitted through Gradescope.

Additional resources

Randomized Numerical Linear Algebra:

Randomized numerical linear algebra: Foundations and algorithms by P.-G. Martinsson and J. A. Tropp
Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions by N. Halko, P. G. Martinsson and J. A. Tropp
Randomized Algorithms for Matrices and Data by M. W. Mahoney
Sketching as a Tool for Numerical Linear Algebra by D. P. Woodruff
An Introduction to Matrix Concentration Inequalities by J. A. Tropp
Randomized algorithms in numerical linear algebra by R. Kannan and S. Vempala

Numerical Linear Algebra:

Numerical linear algebra by L. N. Trefethen and D. Bau, III
Matrix Algorithms Volume 1: Basic Decompositions by G. Stewart
Matrix algorithms volume 2: eigensystems by G. W. Stewart
Matrix computations by G. H. Golub and C. F. Van Loan
Matrix analysis by R. A. Horn and C. R. Johnson
Matrix analysis by R. Bhatia

Probability Theory:

Lecture notes

Lecture 1 [pdf] and [LaTeX]

Lecture 2 [pdf] and [LaTeX]
Further relevant resources:

Lecture 3 [pdf] and [LaTeX]

Lecture 4 [pdf] and [LaTeX]

  • MATLAB code produced in class [MATLAB]

Lecture 5 [pdf] and [LaTeX]

Lecture 6 [pdf] and [LaTeX]

Lecture 7 [pdf] and [LaTeX]

Lecture 8 [pdf] and [LaTeX]

Lecture 9 [pdf]

Lecture 10 [pdf]

Lecture 11 [pdf]

Lecture 12 [pdf] and [LaTeX]

Lecture 13 [pdf] and [LaTeX]

Lecture 14 [pdf] and [LaTeX]

Lecture 15 [pdf] and [LaTeX]

Lecture 16 [pdf] and [LaTeX] (Annotated version: pdf)

Lecture 17 [pdf] and [LaTeX]
Further relevant resources (in no particular order):

Lecture 18 [pdf] and [LaTeX]

Lecture 19 [pdf] and [LaTeX]

Lecture 20 [pdf] and [LaTeX]

Lecture 21 [pdf] and [LaTeX]

  • MATLAB code produced in class [MATLAB]

Further relevant resources (in no particular order):

Lecture 22 [pdf] and [LaTeX]

Lecture 23 [pdf] and [LaTeX]

Homework Assignments

Latex example: [zip]

Homework assignemnt 1: [pdf] and [LaTeX]

Homework assignemnt 2: [pdf] and [LaTeX]

Homework assignemnt 3: [pdf] and [LaTeX]

Homework assignemnt 4: [pdf] and [LaTeX]