In Xanadu did Kubla Khan
A stately pleasure-dome decree:
Where Alph, the sacred river, ran
Through caverns measureless to man
Down to a sunless sea.
So twice five miles of fertile ground
With walls and towers were girdled round:
And there were gardens bright with sinuous rills,
Where blossomed many an incense-bearing tree;
And here were forests ancient as the hills,
Enfolding sunny spots of greenery.
But oh! that deep romantic chasm which slanted
Down the green hill athwart a cedarn cover!
A savage place! as holy and enchanted
As e'er beneath a waning moon was haunted
By woman wailing for her demon-lover!
And from this chasm, with ceaseless turmoil seething,
As if this earth in fast thick pants were breathing,
A mighty fountain momently was forced:
Amid whose swift half-intermitted burst
Huge fragments vaulted like rebounding hail,
Or chaffy grain beneath the thresher's flail:
And 'mid these dancing rocks at once and ever
It flung up momently the sacred river.
Five miles meandering with mazy motion
Through wood and dale the sacred river ran,
Then reached the caverns measureless to man,
And sank in tumult to a lifeless ocean:
And 'mid this tumult Kubla heard from far
Ancestral voices prophesying war!
The shadow of the dome of pleasure
Floated midway on the waves;
Where was heard the mingled measure
From the fountain and the caves.
It was a miracle of rare device,
A sunny pleasure-dome with caves of ice!
A damsel with a dulcimer
In a vision once I saw:
It was an Abyssinian maid,
And on her dulcimer she played,
Singing of Mount Abora.
Could I revive within me
Her symphony and song,
To such a deep delight 'twould win me,
That music loud and long,
I would build that dome in air,
That sunny dome! those caves of ice!
And all who heard should see them there,
And all should cry, Beware! Beware!
His flashing eyes, his floating hair!
Weave a circle round him thrice,
And close your eyes with holy dread,
For he on honey-dew hath fed,
And drunk the milk of Paradise.
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In Stanford U did Golub Gene
A stable SVD decree:
Where U and Sigma V are seen
Through algorithms fast and keen
For matrices in ℂ.
So twice five eps of rounding down
The walls of Jordan blocks were found
By algorithms bright with singular vals,
Where blossomed many an open-source code tree;
And here were methods ancient as the hills,
Enfolding complex space with unit'ry.
But oh! that Schur decomposition which slanted
Down diagonal athwart a strictly upper!
Oh wild subspace! as invariantly recanted
As e're beneath a failing code was haunted
By woman wailing for a better solver!
And from Schur chasm with ceaseless problem solving,
As if this earth for fast methods were calling,
A mighty man, Gene, momently was forced:
From he whose swift intellectual burst
Gave rise to papers like resounding fire,
Came math ingrained into minds inspired:
And for all matrices at once and ever,
The bright SVD. Oh what a solver!
For while meandering with slow convergence
The Power Method pre-Hessenberg ran,
Then reached eig ratios measureless to man,
And sank in tumult to a poor solution:
And 'mid this tumult Golub heard from far
Eigenvals calling for acc'rate QR!
The shadow of results we treasure,
Floating points in error seen;
'Til the err by math was measured
From the fountain pen of Gene.
It was a miracle of rare device,
A wond'rous SVD in software freeze!
A damsel with a dual chip core
In a vision once I saw:
It was by math'matician made,
And on her dual chip core she played,
Singing of MATLAB aura.
Could I revive within me
Her symphony and song,
To such a deep delight 'twould win me,
That with mathematics strong,
I would build in code low err,
That final code! the software freeze!
And all who heard should see Gene there,
And all should cry, Least Squares! Software!
His flashing eyes, his silver hair!
We've a close community,
And note his mark: gentility,
For he our field of labor led,
And wrote the math of Paradise.
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