# Poems

- The Ballad of James Weldon Demmel (Beresford Parlett)
- The Lore Ax=b (Erin Carson)
- Berkeley Zoo (Tim
Davis)

[Dramatic reading (YouTube) / Slides]

## The Ballad of James Weldon Demmel

by Beresford Parlett

with apologies to the poet Longfellow and Hiawatha

Two older friends had Weldon Demmel

Bound to him in closest union. And

to whom he gave the right hand

of his heart, in joy and sorrow.

Beresford, the curious Briton

And his deep advisor, Velvel.

Straight between them ran the pathway

Never grew the grass upon it.

Referees and jealous colleagues

Could not cause ill will between them.

For they kept each otherâ€™s council

Spake with naked hearts together

Pondering much and much contriving

How to solve our matrix problems.

To help all his people prosper

Jim shared the lead in LAPACK efforts.

He would choose the best of methods

For each type of matrix problem.

Then to implement each method

With respect to all platforms.

But all that work was very easy

Compared to what would follow next.

Testing, testing, always testing,

Until the lambs turn into sheep.

Then comes careful documentation

So the engineers could cope.

With how to use this precious software

To solve their practical equations

And ensure that their designs

Would always turn out to be stable,

But only just—to optimize.

Another issue haunted Demmel

As he surveyed the matrix land.

There were so many naughty problems

Ill-behaved, not dignified.

They would skip, react too sharply

Mis-converge and then mislead.

So the crafty, young Jim Demmel

Took his favorite canoe,

Made of birch-bark in the springtime,

And journeyed ever deeper to

This realm of troubled problems

Getting ever worse and worse.

At least he reached the dreaded chasm

Gateway to the underworld,

From which no person can return.

All the problems here are hopeless,

They can never be restored,

They are warped, defective, crippled

In a word, are SINGULAR.

He perceived that all nice problems

Stay far away from this dread place.

The closer to the chasm the worse the problems are.

Sometime later, Weldon Demmel taught

His people in this way:

Pointed at two (great) big Ms, saying;

If you can form their product quickly

Then you can solve all matrix problems

At this self same rapid rate.

The last exploit of Weldon Demmel

Was to find the primal code,

But this required an inward journey

Where no friends could lend a hand.

He meditated on group structures

To attain to Buddha hood.

He said good-bye to Kathy Yelick,

Bade farewell to Meg and Nate.

Then he ascended to Nirvana

Where ONE is all and all is ONE.

Space has vanished and, at last, No

COMMUNI-CA-TION.

## The Lore Ax=b

by Erin Carson

Dedicated to Jim Demmel on the occasion of his 60th birthday

Inspired by the first lecture of Math 221

A typical day on Soda's fifth floor,

A student approaches and knocks on the door.

Professor Demmel, please help,

the student did plea,

I need to solve the problem Ax=b.

Alright,

he said, with a patient reply,

Just run simple GE if you haven't yet tried.

In terms of computation (ignore moving words),

its runtime is n cubed times constant two-thirds.

That seems like a lot!

, said the student, surprised.

Well perhaps there's another approach we could try.

If your matrix is SPD it is true,

Cholesky will save you a factor of 2.

That's still too expensive for me, I fear,

Since away from the diagonal nonzeros disappear.

Ah,

said the Professor, not all is lost,

There's a banded version with a much cheaper cost.

But since I only change b between solves, if I may,

suggest that I might precompute inverse A?

The inverse is dense and its use will be pesky.

You're better off saving the L from Cholesky.

Hmm,

thought the student, Does it help that I know,

That there are at most seven nonzeros per row?

In that case,

said the Professor, forget methods direct,

As long as A's well-conditioned- have you checked?

Consulting his notes, the student then shared,

Kappa(A) is about the cube root of n squared.

Well in that case, let's just use CG.

In flops it costs n raised to four over three.

That still seems too much,

the student did groan.

Does it help if lambda_min and lambda_max are known?

Professor Demmel pondered, scratching his head.

Are there details the student has still left unsaid?

Perhaps more information will help guide our course,

This linear system - what is its source?

Well I've a cube of metal,

the student replied,

I know T on the surface but I need it inside!

Professor Demmel smiled upon hearing this news,

For there were quite obvious methods to choose.

That's just 3D Poisson, why didn't you say?

call FFT or multigrid and call it a day!