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

Posts 1 - 10 of 12

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In an unpublished 1972 technical report "Conserving confluence curbs ill-condition," Velvel Kahan coined the descriptive term pejorative manifold.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."... 更多内容 >>

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In an unpublished 1972 technical report "Conserving confluence curbs ill-condition," Velvel Kahan coined the descriptive term pejorative manifold.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."... 更多内容 >>

The Jordan Canonical Form Just Doesn’t Compute4

Camille Jordan (1838-1922)... 更多内容 >>

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.... 更多内容 >>

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 =... 更多内容 >>

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.... 更多内容 >>

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.... 更多内容 >>

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.... 更多内容 >>

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. ... 更多内容 >>