# Gene Golub’s 22nd Birthday

Tomorrow, February 29, 2020 would be Gene Golub's 22nd birthday.

### Contents

#### Leap Day

Gene was born on Leap Day, February 29, 1932. So, when his birthday came around only every fourth year, we made an especially big deal out of it.

#### Professor SVD

Perhaps foremost among Gene's many accomplishments is the algorithm to compute the SVD, the singular value decomposition. His California license plate was legend.

#### Image approximation

The animation at the beginning of this blog uses the SVD to compute low-rank approximation of an image. X is a three-dimensional array holding a full color photo of Gene.

   X = imread('GHG.jpg');
[m,n,p] = size(X);
sizeX = [m,n,p]
imshow(X)

sizeX =
259   172     3


Reshape X into a two-dimensional matrix $A$ formed from the red, green and blue components.

   A = reshape(X,m,n*p);
sizeA = [m,n*p]
imshow(A)

sizeA =
259   516


Compute the SVD of this wide matrix.

   [U,S,V] = svd(double(A));


Use the SVD to generate low-rank approximations, which are then reshaped to full color.

   for r = 2:2:50
k = 1:r;
B = U(:,k)*S(k,k)*V(:,k)';
B = reshape(B,m,n,p);
imshow(B/256)
end


This is not a particularly good image compression scheme, nevertheless I think two aspects are amazing. The approximations retain the RGB components. And, relatively low rank produces recognizable images. By rank 50 we can read the white board in the background and see his checkered shirt.

#### Stanford CompMath 50

In March, 2007, there was a workshop at Stanford celebrating Gene's 75th birthday, as well as a half-century of Computational Mathematics at Stanford. These coffee mugs, with photos of Golub and George Forsythe, were mementos.

#### NA Digest

Later that year, we put out a special edition of the NA Digest.

From: Cleve Moler <Cleve.Moler@mathworks.com>
Date: Fri, 16 Nov 2007 17:55:42 -0500
Subject: Gene Golub, 1932 - 2007
Gene Golub, founder of the NA Digest, passed away today, Friday, November 16,
at the Stanford University Hospital. He was 75 years old.
Gene returned home to Stanford recently from a trip to Hong Kong. He was
planning to leave again Tuesday on another trip, this one to Zurich where the
ETH was to honor him with a special degree. Instead, Sunday night he went to
the emergency room because he was "feeling lousy". On Tuesday, he was found
to have AML, acute myelogenous leukemia, a form of cancer that affects the
white blood cells. This is a potentially curable disease and he was expecting
to begin chemotherapy today. But serious complications developed suddenly
over night.
I was able to see Gene for an hour last night and he was in reasonably good
spirits. Mike Saunders was trying to get Gene's laptop to use dial-up over
the hospital's phone system because Gene said he was a couple of days behind
on his email. I was planning to get a wireless card for his machine today.
None of us had any idea how suddenly the situation would worsen.
The Stanford iCME students have created a memorial blog at
http://genehgolub.blogspot.com .
Our community has lost its foremost member. He was a valued colleague and
friend. Goodbye, Gene.
-- Cleve Moler

I wrote a short bio for the National Academy of Engineering memorials NAE Tribute. After summarizing his accomplishments and honors, it concluded:

Everything I have said thus far, however, pales in comparison to Golub's most important characteristic -- his humanity. The numerical analysis and scientific computing community was his family. The closeness and congeniality of this community is due, in large part, to his influence. Thousands of people in dozens of countries knew him simply as "Gene" and visitors to Stanford, particularly young people, often stayed in his home. He remembered everybody's name and their children's birthdays, and he returned visits, traveling frequently to give lectures, attend workshops, or just to see people. His friendships, visits, and e-mails not only led to important algorithms and research papers, but also made the world a more pleasant place.

#### Nature

Nick Trefethen wrote a beautiful tribute for Nature. Fittingly, the subtitle is "Mathematician and godfather of numerical analysis." Here is Nick's last paragraph.

Gene Golub was restless and never entirely happy. He was a demanding friend; behind his back, we all had Gene stories to tell. It was a huge back: Gene was big, dominating any room he was in, and grew more impressive and imposing with the years. Graduate students around the world admired and loved him, and he bought them all dinner when he got the chance. His unexpected death, in Stanford in between speaking at a conference in Hong Kong and flying to Zurich for his eleventh honorary degree, has left the world of numerical analysis orphaned and reverberating.

Published with MATLAB® R2019b

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