Math 464A, Numerical Analysis, Fall, 2016

This is the Math 464A homepage. Consult it from time to time to find useful information for the course. I will include links to the syllabus and other course information.

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Here is a copy of current course information.

• Sample problems for the final.
• Sample problems for the midterm.
• Another good reference is Numerical Mathematics by Quarteroni, Sacco, and Saleri. It is also available on line from the UW Library.
• Numerical Analysis by Ridgway Scott is available on line from the UW Library. I highly recommend it.Numerical Analysis
• Scan of parts of Johnson and Riess.
• Chapter 2 of J&R
• Nonsingularity A proof that Ax=b is uniquely solvable (in the square case) exactly when Ax=0 implies x=0.
• Least squares and normal equations.
• A discussion of the Cholesky factorization.
• One of the books I recommended has disappeared from the library. But you can link to the ebook version Numerical Computing with IEEE Floating Point Arithmetic by Michael Overton.
• Wolfram Alpha is a handy free online tool that you might find useful.
• Some of you have asked about other numerical analysis books. Elementary Numerical Analysis by Conte and DeBoor is a good numerical analysis reference book. It's on course reserve.
• Two documents on norms. norms and norms2
• Scanned images of homework from section 2.1 and section 2.2
• Some of you do not yet have a copy of the text. Here is Scan of the first few pages.
• Notes on Singular Value Decomposition.
• Carl DeBoor on divided differences.
• Class email address is math464a_au16@uw.edu
• Least squares applied to polynomial approximation.
• A discussion of Cauchy sequences can be found in Taylor's book or Folland's book; and also on page 197 of Johnson and Riess. There is a discussion of Newton's method in several variables and Cauchy sequences on pages 194-198 of Johnson and Riess. There will be no problems involving Cauchy sequences on the midterm.
• Wikipedia has an entry on Taylor's theorem, with a statement and proof of the several variable case. It is also stated and proved in most books on advanced calculus such as the books by Gerald Folland and Angus Taylor (not Brook Taylor, for whom the theorem is named). These books are both titled Advanced Calculus.
• A proof of the formula for a sum of powers is in Bernoulli Numbers and the Riemann Zeta Function by B. Sury.
• What Every Computer Scientist Should Know About Floating-Point Arithmetic
• A quote from Richard Hamming: "The purpose of numerical analysis is insight, not numbers."
• SAGE website.
• SageMathCloud is a highly recommended, free, open source computational math software system and SageMathCell an online interactive sophisticated "calculator".
• Syllabus