MATH 6610-01 — Analysis of Numerical Methods I


Fall 2019


Instructor: Akil Narayan
Email: akil(-at-)sci.utah.edu
Office phone: +1 801-581-8984
Office location: WEB 4666, LCB 116
Office hours: MW 10:00am-11:30am (WEB 4666)


Class meeting time: Monday, Wednesday, Friday 11:50am - 12:40pm
Class meeting location: JTB (James Talmage Bldg) 120
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 Never PDF
1 : Basic linear algebra and the SVD September 9, 2019 PDF
2 : Projections and the QR decomposition September 30, 2019 PDF
3 : LU and Cholesky factorizations November 4, 2019 PDF
4 : Approximation techniques December 5, 2019 PDF



Miscellaneous handouts


The following are various relevant handouts.

Description Posting date Download
Sample project submission: Homework 0 August 15, 2019 github
Lecture notes -- Vectors, matrices, and norms August 21, 2019 PDF
Lecture notes -- The SVD August 23, 2019 PDF
Lecture notes -- Projection matrices September 9, 2019 PDF
Lecture notes -- The QR decomposition September 12, 2019 PDF
Lecture notes -- Modified Gram Schmidt September 16, 2019 PDF
Lecture notes -- Householder reflections September 16, 2019 PDF
Lecture notes -- Linear least squares problems September 18, 2019 PDF
Lecture notes -- Condition numbers September 20, 2019 PDF
Lecture notes -- Floating point arithmetic September 25, 2019 PDF
Lecture notes -- Algorithm stabiilty September 27, 2019 PDF
Lecture notes -- LU factorizations October 16, 2019 PDF
Lecture notes -- Pivoted LU factorizations October 16, 2019 PDF
Lecture notes -- Cholesky decompositions October 18, 2019 PDF
Lecture notes -- Eigenvalues October 25, 2019 PDF
Lecture notes -- Rayleigh iteration November 7, 2019 PDF
Lecture notes -- The QR algorithm November 7, 2019 PDF
Lecture notes -- Iterative methods November 13, 2019 PDF
Lecture notes -- Fourier Series November 13, 2019 PDF
Lecture notes -- Polynomial interpolation November 18, 2019 PDF
Lecture notes -- Quadrature November 20, 2019 PDF
Lecture notes -- Numerical differentiation November 20, 2019 PDF



Software


The following are links to software used during class demonstrations.

Description Language Download
In-class demonstrations Python (IPython Notebook) github



Resources

Git (version control)
Latex (typesetting documents)