MATH 6610-01 — Analysis of Numerical Methods I


Fall 2017


Instructor: Akil Narayan
Email: akil(-at-)sci.utah.edu
Office phone: +1 801-581-8984
Office location: WEB 4666 or CSC 214D
Office hours: Wednesday 3-5pm, Thursday 9-11am, and by appointment


Class meeting time: Monday, Wednesday, Friday 11:50am - 12:40pm
Class meeting location: JTB (James Talmage Bldg) 120
Textbook (required): (1) Trefethen and Bau III. "Numerical Linear Algebra", ISBN-10 0-89871-361-7, SIAM (1997).
(2) Isaacson and Keller. "Analysis of Numerical Methods" (revised edition), ISBN-13 978-0-486-68029-3, Dover (1994)


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
1 : Basic linear algebra and the SVD September 8, 2017 PDF
2 : Projections, orthogonalization, and least-squares October 2, 2017 PDF
3 : LU and Cholesky factorizations November 1, 2017 PDF
3 : Approximation techniques December 1, 2017 PDF



Miscellaneous handouts


The following are various relevant handouts.

Description Posting date Download
Lecture 1 notes -- Vectors, matrices, and norms August 23, 2017 PDF
Lecture 2 notes -- The SVD August 25, 2017 PDF
Lecture 4 notes -- Projection matrices September 8, 2017 PDF
Lecture 5 notes -- The QR decomposition September 11, 2017 PDF
Lecture 6 notes -- Modified Gram-Schmidt September 13, 2017 PDF
Lecture 7 notes -- Householder transformations September 15, 2017 PDF
Lecture 8 notes -- Linear least-squares September 18, 2017 PDF
Lecture 10 notes -- Conditioning September 22, 2017 PDF
Lecture 11 notes -- Floating-point representation September 25, 2017 PDF
Lecture 12 notes -- Algorithm stability September 27, 2017 PDF
Midterm exam October 16, 2017 PDF
Lecture 13 notes -- The LU decomposition October 17, 2017 PDF
Lecture 14 notes -- Pivoting in LU decompositions October 22, 2017 PDF
Matlab code -- Gram-Schmidt orthogonalization October 22, 2017 ZIP
Matlab code -- LU decompositions October 22, 2017 ZIP
Lecture 16 notes -- Cholesky factorizations October 29, 2017 PDF
Lecture 17 notes -- Eigenvalues October 29, 2017 PDF
Lecture 18 notes -- Power and inverse iteration November 3, 2017 PDF
Lecture 19 notes -- The QR algorithm November 3, 2017 PDF
Lecture 20 notes -- Iterative methods November 12, 2017 PDF
Lecture 21 notes -- Fourier Series November 20, 2017 PDF
Lecture 22 notes -- Polynomial interpolation November 20, 2017 PDF
Lecture 23 notes -- Quadrature November 28, 2017 PDF
Lecture 24 notes -- Numerical differentiation November 30, 2017 PDF
Lecture 25 notes -- Numerical differentiation 2 December 1, 2017 PDF