# Quadruple Precision, 128-bit Floating Point Arithmetic9

Posted by Cleve Moler,

The floating point arithmetic format that occupies 128 bits of storage is known as binary128 or quadruple precision. This blog post describes an implementation of quadruple precision programmed entirely in the MATLAB language.... read more >>

# Apologies to Gram-Schmidt

Posted by Cleve Moler,

This is a follow-up to my previous follow-up, posted several days ago. A very careful reader, Bruno Bazzano, contributed a comment pointing out what he called "a small typo" in my code for the classic Gram-Schmidt algorithm. It is more than a small typo, it is a serious blunder. I must correct the code, then do more careful experiments and reword my conclusions.... read more >>

# Compare Gram-Schmidt and Householder Orthogonalization Algorithms4

Posted by Cleve Moler,

This is a follow-up to my previous post. Classical Gram-Schmidt and Modified Gram-Schmidt are two algorithms for orthogonalizing a set of vectors. Householder elementary reflectors can be used for the same task. The three algorithms have very different roundoff error properties.... read more >>

# Magic Stars

Posted by Cleve Moler,

Magic Stars are a little like Magic Squares. My grandson was introduced to them in his junior high school math class.... read more >>

# Magic Squares Meet Supercomputing

Posted by Cleve Moler,

I have just returned from the huge Supercomputing 2012 conference in Salt Lake City. I can report on interesting reactions to some questions I posed in last week's blog and on some impressive speedup results when we ran the code in last week's blog on a parallel cluster in the Cloud.... read more >>

# Magic Squares, Part 3, Linear Algebra4

Posted by Cleve Moler,

We know a little bit, but not much, about the linear algebraic properties of magic squares. ... read more >>

# Magic Squares, Part 2, Algorithms

Posted by Cleve Moler,

... read more >>

# Magic Squares, Part 1, Low Order1

Posted by Cleve Moler,

With origins in centuries old recreational mathematics, magic squares demonstrate MATLAB array operations. ... read more >>