MATH 6610-01 — Analysis of Numerical Methods I


Fall 2020


Instructor: Akil Narayan
Email: akil(-at-)sci.utah.edu
Office phone: +1 801-581-8984
Office location: WEB 4666, LCB 116
Office hours: Wed 10:45-11:45am, Thu 12pm-1pm (on Zoom)


Class meeting time: Monday, Wednesday, Friday 11:50am - 12:40pm
Class meeting location: Zoom
Textbook (required): Trefethen and Bau III. "Numerical Linear Algebra", ISBN-10 0-89871-361-7, SIAM (1997).


Mathematical analysis of numerical methods in linear algebra, interpolation, integration, differentiation, approximation (including least squares, Fourier analysis, and wavelets), initial- and boundary-value problems of ordinary and partial differential equations

Here are some additional textbook resources (optional) that may be helpful if you're looking for more reading.
  • Demmel. "Applied Numerical Linear Algebra", ISBN-13 978-0898713893, SIAM (1997). This book has many similarities to the Trefethen book, but has more details on numerical linear algebra algorithms.
  • Golub and Van Loan. "Matrix Computations", ISBN-13 978-0801854149, Johns Hopkins University Press, 3rd edition (1996). This book is an excellent detailed reference, but is not necessarily the best as a first learning resource. It is a fairly comprehensive book for linear algebraic algorithms.
  • Strang. "Linear Algebra and its Applications", ISBN-13 978-0030105678, Brooks Cole, 4th edition (2006). This book has more worked-out explicit examples. It covers many of the topics for this course at a high level, but does not go into as much detail as some other texts.
  • Lax. "Linear Algebra and Its Applications", ISBN-13 978-0471751564, Wiley, second edition (2007). This is an excellent mathematical compendium of linear algebra theory. Many computational algorithms are also treated, but at a more abstract level. This book is a "definition, theorem, proof" mathematical treatment of linear algebra.


The course syllabus is here: PDF



Graded assignments


Individual grades for each assignment will be posted to Canvas. (uNID login required.) Note that the letter grades appearing on Canvas are not representative of predicted final letter grades for the course. Final letter grades will be computed according to the rubric and policies on the syllabus.



Homework assignments


Late work will not be accepted without advance approval from the instructor.

Problem set description Due date Homework
0 : Submission demonstration September 2, 2020 PDF
1 : Basic linear algebra and eigenvalues September 16, 2020 PDF
2 : The SVD and QR factorizations October 5, 2020 PDF
3 : LU and Cholesky factorizations November 6, 2020 PDF
4 : Approximation techniques December 3, 2020 PDF



Miscellaneous handouts


The following are various relevant handouts.

Description Posting date Download
Homework submission instructions August 19, 2020 PDF
Sample project submission: Homework 0 August 19, 2020 github
Lecture 00 slides: Linear algebra preliminaries August 28, 2020 PDF
                             Marked slides from class August 28, 2020 PDF
Lecture 01 slides: Projections and permutations September 2, 2020 PDF
                             Marked slides from class September 2, 2020 PDF
Lecture 02 slides: Eigenvalues September 2, 2020 PDF
                             Marked slides from class September 2, 2020 PDF
Lecture 03 slides: Hermitian matrices September 3, 2020 PDF
                             Marked slides from class September 4, 2020 PDF
Lecture 04 slides: The Courant-Fischer-Weyl variational theorem September 6, 2020 PDF
                             Marked slides from class September 9, 2020 PDF
Lecture 05 slides: Floating-point representations September 6, 2020 PDF
                             Marked slides from class September 11, 2020 PDF
Lecture 06 slides: Problem conditioning September 13, 2020 PDF
                             Marked slides from class September 16, 2020 PDF
Lecture 07 slides: Algorithm stability September 13, 2020 PDF
                             Marked slides from class September 18, 2020 PDF
Lecture 08 slides: The spectral theorem September 20, 2020 PDF
                             Marked slides from class September 21, 2020 PDF
Lecture 09 slides: The singular value decomposition September 20, 2020 PDF
                             Marked slides from class September 23, 2020 PDF
Lecture 10 slides: Low rank approximation September 20, 2020 PDF
                             Marked slides from class September 25, 2020 PDF
Lecture 11 slides: The QR decomposition September 25, 2020 PDF
                             Marked slides from class September 29, 2020 PDF
Lecture 12 slides: Modified Gram-Schmidt September 25, 2020 PDF
                             Marked slides from class September 30, 2020 PDF
Lecture 13 slides: Householder reflectors September 25, 2020 PDF
                             Marked slides from class October 2, 2020 PDF
Lecture 14 slides: Least-squares problems October 2, 2020 PDF
                             Marked slides from class October 9, 2020 PDF
Lecture 15 slides: Gaussian elimination and the LU factorization October 9, 2020 PDF
                             Marked slides from class October 12, 2020 PDF
Lecture 16 slides: LU and pivoting October 9, 2020 PDF
                             Marked slides from class October 14, 2020 PDF
Lecture 17 slides: Cholesky decompositions October 9, 2020 PDF
                             Marked slides from class October 16, 2020 PDF
Lecture 18 slides: Power iteration October 18, 2020 PDF
                             Marked slides from class October 21, 2020 PDF
Lecture 19 slides: Rayleigh iteration October 18, 2020 PDF
                             Marked slides from class October 23, 2020 PDF
Lecture 20 slides: The QR algorithm October 22, 2020 PDF
                             Marked slides from class October 26, 2020 PDF
Lecture 21 slides: The QR algorithm with shifts October 23, 2020 PDF
                             Marked slides from class November 1, 2020 PDF
Lecture 22 slides: Iterative methods for linear equations November 1, 2020 PDF
Lecture 23 slides: Iterative methods for nonlinear equations November 2, 2020 PDF
Lecture 24 slides: Fourier Approximation November 9, 2020 PDF
                             Marked slides from class November 11, 2020 PDF
Lecture 25 slides: Polynomial Approximation, I November 10, 2020 PDF
                             Marked slides from class November 13, 2020 PDF
Lecture 26 slides: Polynomial Approximation, II November 10, 2020 PDF
                             Marked slides from class November 16, 2020 PDF
Lecture 27 slides: Integration/differentiation with polynomial approximations November 15, 2020 PDF
                             Marked slides from class November 21, 2020 PDF
Lecture 28 slides: Rational approximation November 18, 2020 PDF
                             Marked slides from class November 25, 2020 PDF