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Compare Gram-Schmidt and Householder Orthogonalization Algorithms
This is a follow-up to my previous post. Classical Gram-Schmidt and Modified Gram-Schmidt are two algorithms for...
8 years 前
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Householder Reflections and the QR Decomposition
The QR decomposition is often the first step in algorithms for solving many different matrix problems, including linear...
8 years 前
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Matrix Multiplication Flexes House
A new app employs transformations of a graphic depicting a house to demonstrate matrix multiplication....
8 years 前
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The Pentium Papers — My First MATLAB Central Contribution
MATLAB Central is celebrating its 15th birthday this fall. In honor of the occasion, MathWorks bloggers are reminiscing...
8 years 前
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Jim Sanderson, Two Careers: Computational Scientist and Conservationist
Jim Sanderson has had a fascinating professional life. He was my PhD student in math at the University of New Mexico in...
8 years 前
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Bug Report Revives Interest in SVD Option of “Eigshow”
A few days ago we received email from Mike Hennessey, a mechanical engineering professor at the University of St. Thomas...
8 years 前
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Compare Gram-Schmidt and Householder Orthogonalization Algorithms
Classical Gram-Schmidt and Modified Gram-Schmidt are two algorithms for orthogonalizing a set of vectors. Householder...
8 years 前
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The Graeffe Root-Squaring Method for Computing the Zeros of a Polynomial
At a minisymposium honoring Charlie Van Loan this week during the SIAM Annual Meeting, I will describe several dubious...
8 years 前
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19 Dubious Ways to Compute the Zeros of a Polynomial
During the SIAM Annual Meeting this summer in Boston there will be a special minisymposium Wednesday afternoon, July 13,...
8 years 前
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Math and Music
What does $\sqrt[12]{2}$ have to do with music? What are equal temperament and just intonation? How can the MATLAB...
8 years 前
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Modernization of Numerical Integration, From Quad to Integral
The MATLAB functions for the numerical evaluation of integrals has evolved from quad, through quadl and quadgk, to today's...
8 years 前
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Strang and Moler Video Course on Differential Equations
Gil Strang has produced a MOOC-style video course on Differential Equations and Linear Algebra. I have added some videos...
8 years 前
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Further Twists of the Moebius Strip
The equations generating a surf plot of the Moebius strip can be parameterized and the parameters allowed to take on...
8 years 前
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The Eigenwalker Model of the Human Gait
A model of the human gait, developed by Nikolaus Troje, is a five-term Fourier series with vector-valued coefficients that...
8 years 前
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Dark Energy Gravitational Waves
Recent theoretical, observational and computational results establish the possibility that gravitational waves produced by...
8 years 前
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Piet Hein, Super Ellipses and Soma Cubes
An extraordinarily creative Danish mathematician, inventor, and poet who often wrote under the Old Norse pseudonym...
8 years 前
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Investigating the Classic Crossed Ladders Puzzle
Today's blog post is a complete working MATLAB program investigating the crossed ladders problem. Download a copy of the...
8 years 前
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The Classic Crossed Ladders Puzzle
Here is a classic puzzle. A pair of ladders leaning against the sides of an alley form a lopsided cross. Each ladder is...
8 years 前
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How Many Times Should You Shuffle the Cards?
We say that a deck of playing cards is completely shuffled if it is impossible to predict which card is coming next when...
8 years 前
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Perfect Shuffles of Playing Cards
When a deck of playing cards is shuffled perfectly, the result is not random. A perfect shuffle places the cards in a...
8 years 前
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Fractal Global Behavior of Newton’s Method
When the starting point of Newton's method is not close to a zero of the function, the global behavior can appear to be...
8 years 前
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Testing Zero Finders
Use the historic cubic polynomial $x^3 - 2x - 5$ to test a few zero-finding algorithms. ...
8 years 前
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A Historic Cubic
The cubic polynomial $x^3 - 2x - 5$ has a unique place in the history of numerical methods....
8 years 前
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John Todd, Savior of Oberwolfach
This is the story of how John Todd saved what was to become one of the world's most important research institutions from...
8 years 前
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Trip Report: SuperComputing 2015
SC15, the International Conference for High Performance Computing, Networking, Storage and Analysis, was held in Austin,...
8 years 前
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Zeroin, Part 3: MATLAB Zero Finder, FZERO
MATLAB adds capability to search for an interval with a sign change....
8 years 前
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Zeroin, Part 2: Brent’s Version
Richard Brent's improvements to Dekker's zeroin algorithm, published in 1971, made it faster, safer in floating point...
9 years 前
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Zeroin, Part 1: Dekker’s Algorithm
Th. J. Dekker's zeroin algorithm from 1969 is one of my favorite algorithms. An elegant technique combining bisection and...
9 years 前
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Charles Lawson, 1931 – 2015
Chuck Lawson passed away in July at the age of 83. Chuck was one of the people who introduced me to computing and...
9 years 前
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Trip Report: Trefethen Birthday Conference
"New Directions in Numerical Computation" was a conference in celebration of Nick Trefethen's 60th birthday held August...
9 years 前
