horror_matrices

Jabberwocky, by Lewis Carroll.

'Twas brillig, and the slithy toves

Did gyre and gimble in the wabe;

All mimsy were the borogoves,

And the mome raths outgrabe.

'Beware the Jabberwock, my son!
The jaws that bite, the claws that catch!
Beware the Jubjub bird, and shun
The frumious Bandersnatch!'

He took his vorpal sword in hand:
Long time the manxome foe he sought--
So rested he by the Tumtum tree,
And stood awhile in thought.

And as in uffish thought he stood,
The Jabberwock, with eyes of flame,
Came whiffling through the tulgey wood,
And burbled as it came!

One, two! One, two! And through and through
The vorpal blade went snicker-snack!
He left it dead, and with its head
He went galumphing back.

'And hast thou slain the Jabberwock?
Come to my arms, my beamish boy!
O frabjous day! Callooh! Callay!'
He chortled in his joy.

'Twas brillig, and the slithy toves
Did gyre and gimble in the wabe;
All mimsy were the borogoves,
And the mome raths outgrabe.

Postal regulations in the United Kingdom prohibit the sending of “Horror comics and matrices” in regular mail. So what is a Horror Matrix? See below for my interpretation.

On the left is “The Jabberwock,” by Sir John Tenniel. Below is the west0479 matrix, which is well behaved for direct methods but a horror matrix for iterative solvers. Try "load west0479" in MATLAB. It comes from a chemical engineering application, but doesn't it look like it has claws? And a spiky tail?

Horror Matrices, by Tim Davis.

`Twas fill-in, and the slow transpose

Did dir'ect factor in archive

All tipsy were the banded 'ones

And memory paths outgave.

"Beware the 'OrrorMat, my son!
The cols that peak, the try's that catch!
Beware the Netlib blurb, and shun
the fractal banded mats!"

He took his direct slash in hand:
Long time the max cond foe he sought ---
So rested he by the elim' tree
And stood while(1) in thought.

And as in out-core work he stood,
The 'OrrorMat, with speyes of NaN,
Came loading through the world-wide web
And core dumped as it ran!

For one! to n! and 'til the end
The direct slash went snicker-snack!
He left it tril, and with diag
He went condesting back.

"And hast thou slain the 'OrrorMat?
Gzip to tars, my direct code!
O fact'rize day! tril(U)! tril(A)!"
He posted in his ode.

`Twas fill-in, and the slow transpose
Did dir'ect factor in archive
All tipsy were the banded 'ones
And memory paths outgave.