MATH 6610-01 — Analysis of Numerical Methods I
Fall 2017
Instructor: |
Akil Narayan |
Email: |
akilsci.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
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Due date
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Homework
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1 : Basic linear algebra and the SVD
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September 8, 2017
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PDF
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2 : Projections, orthogonalization, and least-squares
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October 2, 2017
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PDF
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3 : LU and Cholesky factorizations
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November 1, 2017
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PDF
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3 : Approximation techniques
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December 1, 2017
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PDF
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Miscellaneous handouts
The following are various relevant handouts.
Description
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Posting date
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Download
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Lecture 1 notes -- Vectors, matrices, and norms
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August 23, 2017
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PDF
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Lecture 2 notes -- The SVD
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August 25, 2017
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PDF
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Lecture 4 notes -- Projection matrices
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September 8, 2017
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PDF
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Lecture 5 notes -- The QR decomposition
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September 11, 2017
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PDF
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Lecture 6 notes -- Modified Gram-Schmidt
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September 13, 2017
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PDF
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Lecture 7 notes -- Householder transformations
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September 15, 2017
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PDF
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Lecture 8 notes -- Linear least-squares
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September 18, 2017
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PDF
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Lecture 10 notes -- Conditioning
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September 22, 2017
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PDF
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Lecture 11 notes -- Floating-point representation
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September 25, 2017
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PDF
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Lecture 12 notes -- Algorithm stability
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September 27, 2017
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PDF
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Midterm exam
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October 16, 2017
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PDF
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Lecture 13 notes -- The LU decomposition
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October 17, 2017
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PDF
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Lecture 14 notes -- Pivoting in LU decompositions
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October 22, 2017
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PDF
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Matlab code -- Gram-Schmidt orthogonalization
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October 22, 2017
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ZIP
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Matlab code -- LU decompositions
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October 22, 2017
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ZIP
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Lecture 16 notes -- Cholesky factorizations
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October 29, 2017
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PDF
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Lecture 17 notes -- Eigenvalues
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October 29, 2017
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PDF
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Lecture 18 notes -- Power and inverse iteration
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November 3, 2017
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PDF
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Lecture 19 notes -- The QR algorithm
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November 3, 2017
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PDF
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Lecture 20 notes -- Iterative methods
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November 12, 2017
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PDF
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Lecture 21 notes -- Fourier Series
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November 20, 2017
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PDF
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Lecture 22 notes -- Polynomial interpolation
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November 20, 2017
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PDF
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Lecture 23 notes -- Quadrature
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November 28, 2017
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PDF
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Lecture 24 notes -- Numerical differentiation
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November 30, 2017
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PDF
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Lecture 25 notes -- Numerical differentiation 2
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December 1, 2017
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PDF
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