During the SIAM Annual Meeting this summer in Boston there will be a special minisymposium Wednesday afternoon, July 13, honoring Charlie Van Loan, who is retiring at Cornell. (I use "at" because he's not leaving Ithaca.) I will give a talk titled "19 Dubious Way to Compute the Zeros of a Polynomial", following in the footsteps of the paper about the matrix exponential that Charlie and I wrote in 1978 and updated 25 years later. I really don't have 19 ways to compute polynomial zeros, but then I only have a half hour for my talk. Most of the methods have been described previously in this blog. Today's post is mostly about "roots".... 続きを読む >>

The MATLAB functions for the numerical evaluation of integrals has evolved from quad, through quadl and quadgk, to today's integral. ... 続きを読む >>

When the starting point of Newton's method is not close to a zero of the function, the global behavior can appear to be unpredictable. Contour plots of iteration counts to convergence from a region of starting points in the complex plane generate thought-provoking fractal images. Our examples employ the subject of two recent posts, the historic cubic $x^3-2x-5$. ... 続きを読む >>

Use the historic cubic polynomial $x^3 - 2x - 5$ to test a few zero-finding algorithms. ... 続きを読む >>

The cubic polynomial $x^3 - 2x - 5$ has a unique place in the history of numerical methods.... 続きを読む >>

MATLAB adds capability to search for an interval with a sign change.... 続きを読む >>

Richard Brent's improvements to Dekker's zeroin algorithm, published in 1971, made it faster, safer in floating point arithmetic, and guaranteed not to fail. ... 続きを読む >>

Th. J. Dekker's zeroin algorithm from 1969 is one of my favorite algorithms. An elegant technique combining bisection and the secant method for finding a zero of a function of a real variable, it has become fzero in MATLAB today. This is the first of a three part series.... 続きを読む >>

Chuck Lawson passed away in July at the age of 83. Chuck was one of the people who introduced me to computing and mathematical software. I worked for him at Caltech's Jet Propulsion Laboratory during the summers of 1961 and 1962, just before and after my first year in grad school.... 続きを読む >>

"New Directions in Numerical Computation" was a conference in celebration of Nick Trefethen's 60th birthday held August 25-28 in the new Andrew Wiles building, which houses the Mathematical Institute of the University of Oxford.... 続きを読む >>