# Cleve’s Corner: Cleve Moler on Mathematics and ComputingScientific computing, math & more

Posts 1 - 10 of 13

# My Chat With ChatGPT5

While it is still fresh in my mind, I want to describe the conversation I had with a publicly available version of ChatGPT, the much-discussed large language model, LLM, for conversational artificial intelligence.... read more >>

# Pejorative Manifolds of Polynomials and Matrices, part 2

In an unpublished 1972 technical report "Conserving confluence curbs ill-condition," Velvel Kahan coined the descriptive term pejorative manifold. In case you don't use it in everyday conversation, pejorative means "expressing contempt or disapproval."... read more >>

# Pejorative Manifolds of Polynomials and Matrices, part 12

In an unpublished 1972 technical report "Conserving confluence curbs ill-condition," Velvel Kahan coined the descriptive term pejorative manifold. In case you don't use it in everyday conversation, pejorative means "expressing contempt or disapproval."... read more >>

# The Jordan Canonical Form Just Doesn’t Compute4

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

# The MATLAB Technical Computing Environment2

The ACM Special Interest Group on Programming Languages, SIGPLAN, expects to hold the fourth in a series of conferences on the History of Programming Languages in 2020, see HOPL-IV. The first drafts of papers are to be submitted by August 2018. That long lead time gives me the opportunity to write a detailed history of MATLAB. I plan to write the paper in sections, which I'll post in this blog as they are available. This is the seventh, and final, installment.... read more >>

# Happy Pi Day

Pi DayHappy Pi Day, 3/14.Here are 10,000 digits of π. Notice the six consecutive 9's in the sixth row, digits 763 through 768. n = 100; % Get pi from Symbolic Toolbox. p =... read more >>

# How Far Apart Are Two Random Points in a Hypercube?3

Two days ago I wrote about random points in a square. At the last minute I added the paragraph asking about the generalization to random points in a cube. I have to admit that I didn't check the Web to see what was known about the question.... read more >>

# How Far Apart Are Two Random Points in a Square?5

How far apart can you expect two points chosen at random in the unit square to be? I found this problem on the YouTube channel maintained by Presh Talwalkar, Mind Your Decisions. He correctly calls it a very hard puzzle. At first, I guessed the answer might be $1/2$. But the correct answer is more interesting than that.... read more >>

# Hilbert Matrices6

I first encountered the Hilbert matrix when I was doing individual studies under Professor John Todd at Caltech in 1960. It has been part of my professional life ever since.... read more >>

# 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 integral. ... read more >>

Posts 1 - 10 of 13