Let me tell you about MATLAB's controversial function `rat`.... read more >>

# Continued Fractions and Function “rat” 1

Posted by **Cleve Moler**,

**Category:**- Fun,
- History,
- Numerical Analysis,
- Precision

Blogs

Posted by **Cleve Moler**,

Let me tell you about MATLAB's controversial function `rat`.... read more >>

**Category:**- Fun,
- History,
- Numerical Analysis,
- Precision

Posted by **Cleve Moler**,

*This post is by my colleague Cosmin Ionita.*... read more >>

**Category:**- Algorithms,
- Calculus,
- Numerical Analysis

Posted by **Cleve Moler**,

For the past month I have been working with the variable format 16-bit floating point arithmetic that I described in this post. It has been frustrating work. I have found that the limited precision and limited range of half precision make it barely usable for the kind of experiments with matrix computation that I like to do. In this post I will describe a few of these experiments.... read more >>

**Category:**- Eigenvalues,
- Matrices,
- Numerical Analysis,
- Precision

Posted by **Cleve Moler**,

In a comment following my post about half-precision arithmetic, "Raj C" asked how the parameters for IEEE Standard 754 floating point arithmetic were chosen. I replied that I didn't know but would try to find out. I called emeritus U. C. Berkeley Professor W. (Velvel) Kahan, who was the principle architect of 754. Here is what I learned.... read more >>

**Category:**- Numerical Analysis,
- People,
- Precision

Posted by **Cleve Moler**,

A year and a half ago I wrote a post about "half precision" 16-bit floating point arithmetic, Moler on fp16. I followed this with a bug fix, bug in fp16. Both posts were about *fp16*, defined in IEEE standard 754. This is only one of 15 possible 16-bit formats. In this post I am going to consider all 15.... read more >>

**Category:**- Numerical Analysis,
- Precision

Posted by **Cleve Moler**,

As the degree of an interpolating polynomial increases, does the polynomial converge to the underlying function? The short answer is maybe. I want to describe a visual tool to help you investigate this question yourself.... read more >>

**Category:**- Calculus,
- Numerical Analysis,
- People

Posted by **Cleve Moler**,

I probably first saw this matrix in 1960 in John Todd's class at Caltech. But I forgot about it until Tahar Loulou jogged my memory with a comment following my blog post in late May. It deserves a place in our gallery of interesting matrices.... read more >>

**Category:**- History,
- Matrices,
- Numerical Analysis,
- People

Posted by **Cleve Moler**,

Camille Jordan (1838-1922)... read more >>

**Category:**- Eigenvalues,
- History,
- Matrices,
- Numerical Analysis,
- Symbolic

Posted by **Cleve Moler**,

The Wikipedia article on Pascal's Triangle has hundreds of properties of the triangle and there are dozens of other Web pages devoted to it. Here are a few facts that I find most interesting.
... read more >>

**Category:**- Fun,
- Matrices,
- Numerical Analysis

Posted by **Cleve Moler**,

In the 1970s and early 1980s, while I was working on the LINPACK and EISPACK projects that I discussed in two previous posts, I was a Professor of Mathematics and then of Computer Science at the University of New Mexico in Albuquerque. I was teaching courses in Linear Algebra and Numerical Analysis. I wanted my students to have easy access to LINPACK and EISPACK without writing Fortran programs. By "easy access" I meant not going through the remote batch processing and the repeated edit-compile-link-load-execute process that was ordinarily required on the campus central mainframe computer.... read more >>

**Category:**- History,
- Matrices,
- Numerical Analysis

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