Published

Brad Efron’s Nontransitive Dice
Do not get involved in a bar bet with Brad Efron and his dice until you have read this....

8 years ago

Published

C^5, Cleve’s Corner Collection Card Catalog
I have been writing books, programs, newsletter columns and blogs since 1990. I have now collected all of this material...

8 years ago

Published

Levenshtein Edit Distance Between Strings
How can you measure the distance between two words? How can you find the closest match to a word in a list of words? The...

8 years ago

Published

Latent Semantic Indexing, SVD, and Zipf’s Law
Latent Semantic Indexing, LSI, uses the Singular Value Decomposition of a term-by-document matrix to represent the...

8 years ago

Published

What is the Condition Number of a Matrix?
A couple of questions in comments on recent blog posts have prompted me to discuss matrix condition numbers.... read more...

8 years ago

Published

Householder Seminar HHXX on Numerical Linear Algebra
The Householder meetings on Numerical Linear Algebra have been held roughly every three years since 1961. The twentieth,...

8 years ago

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Hilbert Matrices
I first encountered the Hilbert matrix when I was doing individual studies under Professor John Todd at Caltech in 1960. It...

8 years ago

Published

Quadruple Precision, 128-bit Floating Point Arithmetic
The floating point arithmetic format that occupies 128 bits of storage is known as binary128 or quadruple precision. This...

8 years ago

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“Half Precision” 16-bit Floating Point Arithmetic
The floating point arithmetic format that requires only 16 bits of storage is becoming increasingly popular. Also known as...

8 years ago

Published

A Roman Numeral Object, with Arithmetic, Matrices and a Clock
A MATLAB object for arithmetic with Roman numerals provides an example of object oriented programming. I had originally...

8 years ago

Published

Bank Format and Metric Socket Wrenches
A report about a possible bug in format bank and a visit to a local hardware store made me realize that doing decimal...

8 years ago

Published

My Erdös Number and My Trump Number
I've long known that my Erdös Number is 3. This means that the length of the path on the graph of academic coauthorship...

8 years ago

Published

Morse Code, Binary Trees and Graphs
A binary tree is an elegant way to represent and process Morse code. The new MATLAB graph object provides an elegant way to...

8 years ago

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Lake Arrowhead Coauthor Graph Revisited
The Lake Arrowhead Coauthor Graph came out of the Householder XII conference in 1993 at the UCLA conference center in the...

8 years ago

Published

Hypercubes and Graphs
The adjacency matrix of a hypercube demonstrates the new MATLAB graph object....

9 years ago

Published

Patience Chinese Rings Puzzle
MIT's Professor Daniel Frey recently introduced me to an ancient mechanical puzzle known as "Chinese Rings", "Patience", or...

9 years ago

Published

Ulps Plots Reveal Math Function Accuracy
"ULP" stands for "unit in the last place." An ulps plot samples a fundamental math function such as $\sin{x}$, or a more...

9 years ago

Published

Fitting and Extrapolating US Census Data
A headline in the New York Times at the end of 2016 said "Growth of U.S. Population Is at Slowest Pace Since 1937". This...

9 years ago

Published

Season’s Greetings Fractal
I don't recall where I found this seasonal fractal. And I can't explain how it works. So please submit a comment if you can...

9 years ago

Published

My First Matrix, RGB, YIQ, and Color Cubes
When I was in high school in the 1950's, I didn't know anything about matrices. But I nearly encountered one when I wrote a...

9 years ago

Published

Four Fundamental Subspaces of Linear Algebra, Corrected
(Please replace the erroneous posting from yesterday, Nov. 28, with this corrected version.)...

9 years ago

Published

Four Fundamental Subspaces of Linear Algebra
Here is a very short course in Linear Algebra. The Singular Value Decomposition provides a natural basis for Gil Strang's...

9 years ago

Published

My Favorite ODE
My favorite ordinary differential equation provides a good test of ODE solvers, both numeric and symbolic. It also provides...

9 years ago

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Introducing Cleve’s Laboratory
I am launching a project that I call Cleve's Laboratory. My most recent Cleve's Corner column in MathWorks News & Notes...

9 years ago

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Apologies to Gram-Schmidt
This is a follow-up to my previous follow-up, posted several days ago. A very careful reader, Bruno Bazzano, contributed a...

9 years ago

Published

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...

9 years ago

Published

Householder Reflections and the QR Decomposition
The QR decomposition is often the first step in algorithms for solving many different matrix problems, including linear...

9 years ago

Published

Matrix Multiplication Flexes House
A new app employs transformations of a graphic depicting a house to demonstrate matrix multiplication....

9 years ago

Published

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...

9 years ago

Published

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...

9 years ago