For several years we thought Hadamard matrices showed maximum element growth for Gaussian elimination with complete pivoting. We were wrong.... read more >>

# Complete Pivoting and Hadamard Matrices 1

Posted by **Cleve Moler**,

Posted by **Cleve Moler**,

For several years we thought Hadamard matrices showed maximum element growth for Gaussian elimination with complete pivoting. We were wrong.... read more >>

Posted by **Cleve Moler**,

In rare cases, Gaussian elimination with partial pivoting is unstable. But the situations are so unlikely that we continue to use the algorithm as the foundation for our matrix computations.... read more >>

Posted by **Cleve Moler**,

Denormal floating point numbers and gradual underflow are an underappreciated feature of the IEEE floating point standard. Double precision denormals are so tiny that they are rarely numerically significant, but single precision denormals can be in the range where they affect some otherwise unremarkable computations. Historically, gradual underflow proved to be very controversial during the committee deliberations that developed the standard.... read more >>

Posted by **Cleve Moler**,

This is the first part of a two-part series about the single- and double precision floating point numbers that MATLAB uses for almost all of its arithmetic operations. (This post is adapted from section 1.7 of my book Numerical Computing with MATLAB, published by MathWorks and SIAM.)... read more >>

Posted by **Cleve Moler**,

The nineteenth Householder Symposium, Householder XIX, was held June 8-13 at Sol Cress, a conference center near Spa, Belgium. If you have been following either the web or the newletter edition of Cleve's Corner you know that the Gatlinburg/Householder series of conferences have played an important role in both my professional life and the history of MATLAB. I attended what turned out to be the third conference in the series, in Gatlinburg, Tennesse, when I was a graduate student in 1964. I have been to all 17 of the conferences that have been held since 1964. Here is a link to my News and Notes article about the Gatlinburg/Householder conferences.... read more >>

Posted by **Cleve Moler**,

Stiffness is a subtle concept that plays an important role in assessing the effectiveness of numerical methods for ordinary differential equations. (This article is adapted from section 7.9, "Stiffness", in *Numerical Computing with MATLAB*.)... read more >>

Posted by **Cleve Moler**,

The functions `ode23` and `ode45` are the principal MATLAB and Simulink tools for solving nonstiff ordinary differential equations.... read more >>

Posted by **Cleve Moler**,

MATLAB and Simulink have a powerful suite of routines for the numerical solution of ordinary differential equations. Today's post offers an introduction. Subsequent posts will examine several of the routines in more detail.... read more >>

Posted by **Cleve Moler**,

Changing the value of a parameter in the equations that produce the famous Lorenz chaotic attractor yields nonlinear ordinary differential equations that have periodic solutions.... read more >>

Posted by **Cleve Moler**,

The Singular Value Decomposition of the digram frequency matrix of a text coded with a simple substitution cypher can reveal information about the vowels and consonants in the text.... read more >>