50/50, 20/20, and Other Golden Ratios

Reflections on a Favorite Collaboration

Charles Van LoanMarch 1, 2008

Books

B1 B2

:::

B17

Conference Papers

C1 C2 :::

C65

Journal Papers

J1 J2

:::

J175

As a collaborator, Gene was unique.

Milestones in Matrix Computation

Golub and de Boor -- Golub and Oliger -- Golub and Van Loan -- Golub and Meurant -- Glowinski, Golub, Meurant and Periaux -- Golub and Van Loan --Golub and Van Dooren -- Golub and Ortega -- Moonen, Golub and DeMoor -- Golub and Ortega -- Golub, Greenbaum and Luskin -- R.Chan, T.Chan and Golub -- Golub and Van Loan -- Gautschi, Golub and Opfer -- Golub and Krukier -- Golub and Saunders -- Bartels, Golub, and Saunders -- Dent and Golub-- Dantzig, Cottle, Eaves, Golub, Hillier, Manne, Wilde, and Wilson -- Golub and Styan -- Golub, Guttman, and Dutter -- Concus and Golub Golub and Pereyra-- Concus, Golub, and O’Leary -- Cline, Golub, and Platznman -- Golub and Luk -- Golub and Underwood -- Buzbee, Golub, and Howell -- Boley and Golub --Boley and Golub -- Dahlquist, Golub, and Nash -- Golub and Van Loan -- Leveque and Golub -- Luk, Golub, and Pagano -- Golub and Plemmons -- Goluband Overton -- T.Chan, Golub, and Leveque -- Golub and Mayers -- Ferziger, Golub, and Thompson -- Golub, Plemmons, and Sameh -- Gander, Golub, and von Matt -- Elman and Golub -- W.Gander, Golub, and Gruntz -- De Pillis and Golub -- Ferng, Golub, and Plemmons -- Boley and Golub -- Elhay, Golub, and Kautsky -- Bojanczyk, Golub, and Van Dooren -- Calvetti, Golub, and Reichel -- Fischer and Golub -- Freund, Golub, and Nachtigal -- Golub and Meurant-- Ernst and Golub -- Golub and Zha -- Golub, Silvester, and Wathen -- Golub and von Matt -- Golub and Van der Vorst -- Golub and van Der Vorst --Chandrasekaran, Golub, Gu, and Sayed -- Golub and von Matt -- Golub, Solna, and van Dooren -- W.Gander and Golub -- Drexler and Golub -- Golub, Nguyan, and Milanfar -- Golub, Nguyan, and Milanfar -- Bai and Golub -- Golub, Milanfar, Putinar, Varah, and Gustafson -- Golub and Vanderstraeten --Engquist and Golub -- Bai and Golub -- Golub, Sun, Folwell, and Li -- M. Gander and Golub -- Golub, Kamvar, Haveliwala, and Manning -- Clayton, Golub, Skare, Modarresi, and Bammer -- Golub and Varga -- Businger and Golub -- Golub and Kahan -- Forsythe and Golub -- Golub and Wilkinson -- Bjorck and Golub -- Golub and Robertson -- Bartels and Golub -- Bartels and Golub -- Bartels and Golub -- Bartels and Golub -- Golub and Welsch -- Businger and Golub -- Golub and Reinsch -- Buzbee, Dorr, Golub, and George -- Golub and Smith -- Dahlquist, Eisenstat, and Golub -- Bjorck and Golub -- Golub and Styan -- Golub and Pereyra Concus and Golub -- Golub and Seneta --Golub and Varah -- Gill, Golub, Murray, and Saunders -- Fischer, Golub, Hald, Leiva, and Widlund -- Golub and Seneta -- Golub, Jennings, and Yang -- Golub and Wilkinson -- Bjorck and Wilkinson -- Concus, Golub, and O’Leary -- de Boor and Golub -- Cottle, Golub, and Sacher -- Golub and langlois -- Golub, Heath, and Wahba -- Golub, Nash, and Van Loan -- Golub and Van Loan -- goluband Plemmons -- Golub and Van Loan -- Golub and Ward -- Golub, Luk, and Overton -- Golub and Tang -- Golub and Nash -- T.Chan, Golub, and LeVeque-- Golub and Kautsky -- Golub and kautsky -- Boley and Golub -- Gallant and Golub -- Boley and Golub -- Concus, Golub, and Meurant -- Golub, Manneback, and Toint -- Golub and Meyer -- Golub and Kannan -- Golub, Hoffman, Stewart -- Boley and Golub -- Arbenz and Golub -- Arbenz, W. Gander, and Golub -- Golub and Overton -- Golub and O’leary -- W. Gander, Golub, and von Matt -- Golub and Kent -- Golub and Gutknecht -- Comon and Golub --Elman and Golub -- Arbenz and Golub -- Berry and Golub -- Boley, Elhay, Golub, and Gutknecht -- de Moor and Golub -- Elhay, Golub, and Kautsky --Elman and Golub -- Ferng, Golub, and Plemmons -- Fischer and Golub -- Freund, Golub, and Nachtigal -- Golub and von Matt -- Boley, Brent, Golub, and Luk-- Carey, Chen, Golub, and Sameh -- Elhay, Golub, and Kautsky -- Elman and Golub -- Fischer and Golub -- Golub, Kagstrom, and van Dooren -- Boley, Golub, Makar, Saxena, and Mc Clsukey -- Golub and Strakos -- Calvetti, Golub, Reichel -- Elman, Golub, and Starke -- Dubrulle and Golub -- Elman and Golub -- W. Gander, Golub, and Strebel -- Golub, Xu, Zha, Kailath -- Golub and Zha -- Carey, Golub, and Law -- Arbenz and Golub -- Golub and Lui -- Chu, Funderlic, and Golub -- Bai, Fahey, and Golub -- Golub, Varadhan, and Berry -- Bai and Golub -- Golub and von matt -- Fierro, Golub, Hansen, and O’Leary -- Chandrasekaran, Golub, Gu, and Sayed -- Chu, Funderlic, and Golub -- Golub and Meurant -- Golub, Zhang, and Law -- Chandrasekaran, Golub, Gu, and Sayed -- Golub, Zhang, and Law -- Golub and Wathen -- Golub, huang, Simon, and Tang -- Golub, Law, and Zhang -- Andersson, Elfving, and Golub --Giladi, Golub, and Keller -- Chandrasekaran, Golub, Gu, and Sayed -- Bablama, Calvetti, Golub, and Reichel -- T. Chan, Golub, and Mulet -- Calvetti, Golub, and Reichel -- Chu, Funderlic, and Golub -- Golub, Zhang, and Law -- Benzi and Golub -- Calvetti, Golub, and Reichel -- Calvetti, Golub, and Reichel --Golub, Hansen, and O’Leary -- Elhay, Gladwell, Golub, and Ram -- Chandrasekaran, Golub, Gu, and Sayed -- Golub and Ye -- Golub, Milanfar, and Varah --Calvetti, Golub, Gragg, and Reichel --van der Vorst and Golub -- Golub, Murphy, and Wathen -- Golub and Ye -- Golub and Vanderstraeten -- Golub, Zhang, and Zha -- Golub, Solna, and van Dooren -- Golub, Sameh, and Sarin -- Golub, Nguyen, and Milanfar -- Golub, Nguyen, and Milanfar -- Golub and Melboe --Golub, Wu, and Yuan -- Golub and Zhang -- Chu and Golub -- Concus, Golub, and Sun -- Golub, Greif, and Varah -- Golub and Yuan -- Elhay, Golub, and Ram -- Golub and Pereyra -- Golub and Greif -- Golub, Orchard, Greif, Bjornson, and Atkins -- Benzi, M. gander, and Golub -- bai, Golub, and Ng -- Alter and Golub -- Benzi and Golub -- Golub, Sima, Van Huffel -- Elad, Golub, and Milanfar -- Bai, Golub, and Pan -- Golub, Kamvar, Haveliwala -- Golub, Yuan, Plemmons, cecAlio -- Golub and Livne -- Golub, Vandebril, Barel, Mastronardi -- Boutry, Elad, Golub, Milanfar -- Golub, Tsaig, Elad, Milanfar -- Golub, Holz, and Law -- Bertaccini, Capizzano, Golub, and Possio -- Capizzano, Bertaccini, and Golub -- Golub, Greif, and Varah -- Benzi, Golub, and Liesen -- Bai, Golub, Lu, and Yin -- Cuyt, Golub, Milanfar, verdonk -- Alter and Golub -- Golub and Liao -- Botchev and Golub -- Golub and de Boor -- Golub and Oliger --Golub and Van Loan -- Golub and Meurant -- Glowinski, Golub, Meurant and Periaux -- Golub and Van Loan -- Golub and Van Dooren -- Golub and Ortega -- Moonen, Golub and DeMoor -- Golub and Ortega -- Golub, Greenbaum and Luskin -- R.Chan, T.Chan and Golub -- Golub and Van Loan -- Gautschi, Golub and Opfer -- Golub and Krukier -- Golub and Saunders -- Bartels, Golub, and Saunders -- Dent and Golub -- Dantzig, Cottle, Eaves, Golub, Hillier, Manne, Wilde, and Wilson -- Golub and Styan -- Golub, Guttman, and Dutter -- Concus and Golub Golub and Pereyra -- Concus, Golub, and O’Leary -- Cline, Golub, and Platznman -- Golub and Luk -- Golub and Underwood -- Buzbee, Golub, and Howell -- Boley and Golub -- Boley and Golub -- Dahlquist, Golub, and Nash -- Golub and Van Loan -- Leveque and Golub -- Luk, Golub, and Pagano -- Golub and Plemmons -- Golub and Overton -- T.Chan, Golub, and Leveque -- Golub and Mayers -- Ferziger, Golub, and Thompson -- Golub, Plemmons, and Sameh -- Gander, Golub, and von Matt -- Elman and Golub --W.Gander, Golub, and Gruntz -- De Pillis and Golub -- Ferng, Golub, and Plemmons -- Boley and Golub -- Elhay, Golub, and Kautsky -- Bojanczyk, Golub, and Van Dooren -- Calvetti, Golub, and Reichel -- Fischer and Golub -- Freund, Golub, and Nachtigal -- Golub and Meurant -- Ernst and Golub -- Golub and Zha -- Golub, Silvester, and Wathen -- Golub and von Matt -- Golub and Van der Vorst -- Golub and van Der Vorst -- Chandrasekaran, Golub, Gu, and Sayed-- Golub and von Matt -- Golub, Solna, and van Dooren -- W.Gander and Golub -- Drexler and Golub -- Golub, Nguyan, and Milanfar -- Golub, Nguyan, and Milanfar -- Bai and Golub -- Golub, Milanfar, Putinar, Varah, and Gustafson -- Golub and Vanderstraeten -- Engquist and Golub -- Bai and Golub -- Golub, Sun, Folwell, and Li -- M. Gander and Golub -- Golub, Kamvar, Haveliwala, and Manning -- Clayton, Golub, Skare, Modarresi, and Bammer -- Golub and Varga -- Businger and Golub -- Golub and Kahan -- Forsythe and Golub -- Golub and Wilkinson -- Bjorck and Golub -- Golub and Robertson -- Bartels and G C G l b d O’L Cli G l b d Pl t G l b d L k G l b d U d d B b G l b d H ll B l d G l b

It is hard to fathom the depthof Gene’s impact...

Golub and de Boor -- Golub and Oliger -- Golub and Van Loan -- Golub and Meurant -- Glowinski, Golub, Meurant and Periaux -- Golub and Van Loan --Golub and Van Dooren -- Golub and Ortega -- Moonen, Golub and DeMoor -- Golub and Ortega -- Golub, Greenbaum and Luskin -- R.Chan, T.Chan and Golub -- Golub and Van Loan -- Gautschi, Golub and Opfer -- Golub and Krukier -- Golub and Saunders -- Bartels, Golub, and Saunders -- Dent and Golub-- Dantzig, Cottle, Eaves, Golub, Hillier, Manne, Wilde, and Wilson -- Golub and Styan -- Golub, Guttman, and Dutter -- Concus and Golub Golub and Pereyra-- Concus, Golub, and O’Leary -- Cline, Golub, and Platznman -- Golub and Luk -- Golub and Underwood -- Buzbee, Golub, and Howell -- Boley and Golub --Boley and Golub -- Dahlquist, Golub, and Nash -- Golub and Van Loan -- Leveque and Golub -- Luk, Golub, and Pagano -- Golub and Plemmons -- Goluband Overton -- T.Chan, Golub, and Leveque -- Golub and Mayers -- Ferziger, Golub, and Thompson -- Golub, Plemmons, and Sameh -- Gander, Golub, and von Matt -- Elman and Golub -- W.Gander, Golub, and Gruntz -- De Pillis and Golub -- Ferng, Golub, and Plemmons -- Boley and Golub -- Elhay, Golub, and Kautsky -- Bojanczyk, Golub, and Van Dooren -- Calvetti, Golub, and Reichel -- Fischer and Golub -- Freund, Golub, and Nachtigal -- Golub and Meurant-- Ernst and Golub -- Golub and Zha -- Golub, Silvester, and Wathen -- Golub and von Matt -- Golub and Van der Vorst -- Golub and van Der Vorst --Chandrasekaran, Golub, Gu, and Sayed -- Golub and von Matt -- Golub, Solna, and van Dooren -- W.Gander and Golub -- Drexler and Golub -- Golub, Nguyan, and Milanfar -- Golub, Nguyan, and Milanfar -- Bai and Golub -- Golub, Milanfar, Putinar, Varah, and Gustafson -- Golub and Vanderstraeten --Engquist and Golub -- Bai and Golub -- Golub, Sun, Folwell, and Li -- M. Gander and Golub -- Golub, Kamvar, Haveliwala, and Manning -- Clayton, Golub, Skare, Modarresi, and Bammer -- Golub and Varga -- Businger and Golub -- Golub and Kahan -- Forsythe and Golub -- Golub and Wilkinson -- Bjorck and Golub -- Golub and Robertson -- Bartels and Golub -- Bartels and Golub -- Bartels and Golub -- Bartels and Golub -- Golub and Welsch -- Businger and Golub -- Golub and Reinsch -- Buzbee, Dorr, Golub, and George -- Golub and Smith -- Dahlquist, Eisenstat, and Golub -- Bjorck and Golub -- Golub and Styan -- Golub and Pereyra Concus and Golub -- Golub and Seneta --Golub and Varah -- Gill, Golub, Murray, and Saunders -- Fischer, Golub, Hald, Leiva, and Widlund -- Golub and Seneta -- Golub, Jennings, and Yang -- Golub and Wilkinson -- Bjorck and Wilkinson -- Concus, Golub, and O’Leary -- de Boor and Golub -- Cottle, Golub, and Sacher -- Golub and langlois -- Golub, Heath, and Wahba -- Golub, Nash, and Van Loan -- Golub and Van Loan -- goluband Plemmons -- Golub and Van Loan -- Golub and Ward -- Golub, Luk, and Overton -- Golub and Tang -- Golub and Nash -- T.Chan, Golub, and LeVeque-- Golub and Kautsky -- Golub and kautsky -- Boley and Golub -- Gallant and Golub -- Boley and Golub -- Concus, Golub, and Meurant -- Golub, Manneback, and Toint -- Golub and Meyer -- Golub and Kannan -- Golub, Hoffman, Stewart -- Boley and Golub -- Arbenz and Golub -- Arbenz, W. Gander, and Golub -- Golub and Overton -- Golub and O’leary -- W. Gander, Golub, and von Matt -- Golub and Kent -- Golub and Gutknecht -- Comon and Golub --Elman and Golub -- Arbenz and Golub -- Berry and Golub -- Boley, Elhay, Golub, and Gutknecht -- de Moor and Golub -- Elhay, Golub, and Kautsky --Elman and Golub -- Ferng, Golub, and Plemmons -- Fischer and Golub -- Freund, Golub, and Nachtigal -- Golub and von Matt -- Boley, Brent, Golub, and Luk-- Carey, Chen, Golub, and Sameh -- Elhay, Golub, and Kautsky -- Elman and Golub -- Fischer and Golub -- Golub, Kagstrom, and van Dooren -- Boley, Golub, Makar, Saxena, and Mc Clsukey -- Golub and Strakos -- Calvetti, Golub, Reichel -- Elman, Golub, and Starke -- Dubrulle and Golub -- Elman and Golub -- W. Gander, Golub, and Strebel -- Golub, Xu, Zha, Kailath -- Golub and Zha -- Carey, Golub, and Law -- Arbenz and Golub -- Golub and Lui -- Chu, Funderlic, and Golub -- Bai, Fahey, and Golub -- Golub, Varadhan, and Berry -- Bai and Golub -- Golub and von matt -- Fierro, Golub, Hansen, and O’Leary -- Chandrasekaran, Golub, Gu, and Sayed -- Chu, Funderlic, and Golub -- Golub and Meurant -- Golub, Zhang, and Law -- Chandrasekaran, Golub, Gu, and Sayed -- Golub, Zhang, and Law -- Golub and Wathen -- Golub, huang, Simon, and Tang -- Golub, Law, and Zhang -- Andersson, Elfving, and Golub --Giladi, Golub, and Keller -- Chandrasekaran, Golub, Gu, and Sayed -- Bablama, Calvetti, Golub, and Reichel -- T. Chan, Golub, and Mulet -- Calvetti, Golub, and Reichel -- Chu, Funderlic, and Golub -- Golub, Zhang, and Law -- Benzi and Golub -- Calvetti, Golub, and Reichel -- Calvetti, Golub, and Reichel --Golub, Hansen, and O’Leary -- Elhay, Gladwell, Golub, and Ram -- Chandrasekaran, Golub, Gu, and Sayed -- Golub and Ye -- Golub, Milanfar, and Varah --Calvetti, Golub, Gragg, and Reichel --van der Vorst and Golub -- Golub, Murphy, and Wathen -- Golub and Ye -- Golub and Vanderstraeten -- Golub, Zhang, and Zha -- Golub, Solna, and van Dooren -- Golub, Sameh, and Sarin -- Golub, Nguyen, and Milanfar -- Golub, Nguyen, and Milanfar -- Golub and Melboe --Golub, Wu, and Yuan -- Golub and Zhang -- Chu and Golub -- Concus, Golub, and Sun -- Golub, Greif, and Varah -- Golub and Yuan -- Elhay, Golub, and Ram -- Golub and Pereyra -- Golub and Greif -- Golub, Orchard, Greif, Bjornson, and Atkins -- Benzi, M. gander, and Golub -- bai, Golub, and Ng -- Alter and Golub -- Benzi and Golub -- Golub, Sima, Van Huffel -- Elad, Golub, and Milanfar -- Bai, Golub, and Pan -- Golub, Kamvar, Haveliwala -- Golub, Yuan, Plemmons, cecAlio -- Golub and Livne -- Golub, Vandebril, Barel, Mastronardi -- Boutry, Elad, Golub, Milanfar -- Golub, Tsaig, Elad, Milanfar -- Golub, Holz, and Law -- Bertaccini, Capizzano, Golub, and Possio -- Capizzano, Bertaccini, and Golub -- Golub, Greif, and Varah -- Benzi, Golub, and Liesen -- Bai, Golub, Lu, and Yin -- Cuyt, Golub, Milanfar, verdonk -- Alter and Golub -- Golub and Liao -- Botchev and Golub -- Golub and de Boor -- Golub and Oliger --Golub and Van Loan -- Golub and Meurant -- Glowinski, Golub, Meurant and Periaux -- Golub and Van Loan -- Golub and Van Dooren -- Golub and Ortega -- Moonen, Golub and DeMoor -- Golub and Ortega -- Golub, Greenbaum and Luskin -- R.Chan, T.Chan and Golub -- Golub and Van Loan -- Gautschi, Golub and Opfer -- Golub and Krukier -- Golub and Saunders -- Bartels, Golub, and Saunders -- Dent and Golub -- Dantzig, Cottle, Eaves, Golub, Hillier, Manne, Wilde, and Wilson -- Golub and Styan -- Golub, Guttman, and Dutter -- Concus and Golub Golub and Pereyra -- Concus, Golub, and O’Leary -- Cline, Golub, and Platznman -- Golub and Luk -- Golub and Underwood -- Buzbee, Golub, and Howell -- Boley and Golub -- Boley and Golub -- Dahlquist, Golub, and Nash -- Golub and Van Loan -- Leveque and Golub -- Luk, Golub, and Pagano -- Golub and Plemmons -- Golub and Overton -- T.Chan, Golub, and Leveque -- Golub and Mayers -- Ferziger, Golub, and Thompson -- Golub, Plemmons, and Sameh -- Gander, Golub, and von Matt -- Elman and Golub --W.Gander, Golub, and Gruntz -- De Pillis and Golub -- Ferng, Golub, and Plemmons -- Boley and Golub -- Elhay, Golub, and Kautsky -- Bojanczyk, Golub, and Van Dooren -- Calvetti, Golub, and Reichel -- Fischer and Golub -- Freund, Golub, and Nachtigal -- Golub and Meurant -- Ernst and Golub -- Golub and Zha -- Golub, Silvester, and Wathen -- Golub and von Matt -- Golub and Van der Vorst -- Golub and van Der Vorst -- Chandrasekaran, Golub, Gu, and Sayed-- Golub and von Matt -- Golub, Solna, and van Dooren -- W.Gander and Golub -- Drexler and Golub -- Golub, Nguyan, and Milanfar -- Golub, Nguyan, and Milanfar -- Bai and Golub -- Golub, Milanfar, Putinar, Varah, and Gustafson -- Golub and Vanderstraeten -- Engquist and Golub -- Bai and Golub -- Golub, Sun, Folwell, and Li -- M. Gander and Golub -- Golub, Kamvar, Haveliwala, and Manning -- Clayton, Golub, Skare, Modarresi, and Bammer -- Golub and Varga -- Businger and Golub -- Golub and Kahan -- Forsythe and Golub -- Golub and Wilkinson -- Bjorck and Golub -- Golub and Robertson -- Bartels and G C G l b d O’L Cli G l b d Pl t G l b d L k G l b d U d d B b G l b d H ll B l d G l b

… for behind each of thesecollaborations is a personal

story, a co-author’sgolden ratio…

…a magic proportion…

…a perfect rectangle …

φ2

51+= 871.61803398 …≈

φ

1

… a host of surprising connections.

Gene’s collaborations will last…

… and be nice to look at.

Gene always brought to the table

a certain kind of infinity…

phi = 1.61803 39887 49894 84820 45868

34365 63811 77203 09179 80576

28621 35448 62270 52604 62818

90244 97072 07204 18939 11374

84754 08807 53868 91752 12663…

UΣ VU Σ VU Σ V U Σ V

U Σ V U Σ V U Σ V

U Σ V U Σ V U Σ V

U Σ V U Σ V U Σ V

U Σ V U Σ V U Σ V

20/20 is in the Mind’s Eye of the Beholder

… and a certain kind of vision.

400 BC…

High impact collaborations have a powerful social dimension…

and require a central figure.

April 2007

Gene had shortcomings…

Not φ -by-1

…but they could be re-scaled.

Some days were greater than perfect…

...,1321,8

13,58,3

5,23,1

2,11

813...618.1 <

He and I had our “ups.”

Some days were less than perfect

...,1321,8

13,58,3

5,23,1

2,11

...618.11321 <

He and I had our “downs.”

1/1 2/1 3/2

Our collaboration was a sequence…

5/3

… and it will continue.

Golub and de Boor -- Golub and Oliger -- Golub and Van Loan -- Golub and Meurant -- Glowinski, Golub, Meurant and Periaux -- Golub and Van Loan -- Golub and Van Dooren -- Golub and Ortega -- Moonen, Golub and DeMoor -- Golub and Ortega -- Golub, Greenbaum and Luskin -- R.Chan, T.Chan and Golub -- Golub and Van Loan -- Gautschi, Golub and Opfer -- Golub and Krukier -- Golub and Saunders -- Bartels, Golub, and Saunders -- Dent and Golub -- Dantzig, Cottle, Eaves, Golub, Hillier, Manne, Wilde, and Wilson -- Golub and Styan -- Golub, Guttman, and Dutter -- Concus and Golub Golub and Pereyra -- Concus, Golub, and O’Leary -- Cline, Golub, and Platznman -- Golub and Luk -- Goluband Underwood -- Buzbee, Golub, and Howell -- Boley and Golub -- Boley and Golub -- Dahlquist, Golub, and Nash -- Golub and Van Loan --Leveque and Golub -- Luk, Golub, and Pagano -- Golub and Plemmons -- Golub and Overton -- T.Chan, Golub, and Leveque -- Golub and Mayers -- Ferziger, Golub, and Thompson -- Golub, Plemmons, and Sameh -- Gander, Golub, and von Matt -- Elman and Golub -- W.Gander, Golub, and Gruntz -- De Pillis and Golub -- Ferng, Golub, and Plemmons -- Boley and Golub -- Elhay, Golub, and Kautsky -- Bojanczyk, Golub, and Van Dooren -- Calvetti, Golub, and Reichel -- Fischer and Golub -- Freund, Golub, and Nachtigal -- Golub and Meurant -- Ernst and Golub -- Golub and Zha -- Golub, Silvester, and Wathen -- Golub and von Matt -- Golub and Van der Vorst -- Golub and van Der Vorst --Chandrasekaran, Golub, Gu, and Sayed -- Golub and von Matt -- Golub, Solna, and van Dooren -- W.Gander and Golub -- Drexler and Golub --Golub, Nguyan, and Milanfar -- Golub, Nguyan, and Milanfar -- Bai and Golub -- Golub, Milanfar, Putinar, Varah, and Gustafson -- Golub and Vanderstraeten -- Engquist and Golub -- Bai and Golub -- Golub, Sun, Folwell, and Li -- M. Gander and Golub -- Golub, Kamvar, Haveliwala, and Manning -- Clayton, Golub, Skare, Modarresi, and Bammer -- Golub and Varga -- Businger and Golub -- Golub and Kahan -- Forsythe and Golub -- Golub and Wilkinson -- Bjorck and Golub -- Golub and Robertson -- Bartels and Golub -- Bartels and Golub -- Bartels and Golub --Bartels and Golub -- Golub and Welsch -- Businger and Golub -- Golub and Reinsch -- Buzbee, Dorr, Golub, and George -- Golub and Smith --Dahlquist, Eisenstat, and Golub -- Bjorck and Golub -- Golub and Styan -- Golub and Pereyra Concus and Golub -- Golub and Seneta --Goluband Varah -- Gill, Golub, Murray, and Saunders -- Fischer, Golub, Hald, Leiva, and Widlund -- Golub and Seneta -- Golub, Jennings, and Yang --Golub and Wilkinson -- Bjorck and Wilkinson -- Concus, Golub, and O’Leary -- de Boor and Golub -- Cottle, Golub, and Sacher -- Golub and langlois -- Golub, Heath, and Wahba -- Golub, Nash, and Van Loan -- Golub and Van Loan -- golub and Plemmons -- Golub and Van Loan --Golub and Ward -- Golub, Luk, and Overton -- Golub and Tang -- Golub and Nash -- T.Chan, Golub, and LeVeque -- Golub and Kautsky --Golub and kautsky -- Boley and Golub -- Gallant and Golub -- Boley and Golub -- Concus, Golub, and Meurant -- Golub, Manneback, and Toint-- Golub and Meyer -- Golub and Kannan -- Golub, Hoffman, Stewart -- Boley and Golub -- Arbenz and Golub -- Arbenz, W. Gander, and Golub-- Golub and Overton -- Golub and O’leary -- W. Gander, Golub, and von Matt -- Golub and Kent -- Golub and Gutknecht -- Comon and Golub --Elman and Golub -- Arbenz and Golub -- Berry and Golub -- Boley, Elhay, Golub, and Gutknecht -- de Moor and Golub -- Elhay, Golub, and Kautsky -- Elman and Golub -- Ferng, Golub, and Plemmons -- Fischer and Golub -- Freund, Golub, and Nachtigal -- Golub and von Matt --Boley, Brent, Golub, and Luk -- Carey, Chen, Golub, and Sameh -- Elhay, Golub, and Kautsky -- Elman and Golub -- Fischer and Golub --Golub, Kagstrom, and van Dooren -- Boley, Golub, Makar, Saxena, and Mc Clsukey -- Golub and Strakos -- Calvetti, Golub, Reichel -- Elman, Golub, and Starke -- Dubrulle and Golub -- Elman and Golub -- W. Gander, Golub, and Strebel -- Golub, Xu, Zha, Kailath -- Golub and Zha --Carey, Golub, and Law -- Arbenz and Golub -- Golub and Lui -- Chu, Funderlic, and Golub -- Bai, Fahey, and Golub -- Golub, Varadhan, and Berry -- Bai and Golub -- Golub and von matt -- Fierro, Golub, Hansen, and O’Leary -- Chandrasekaran, Golub, Gu, and Sayed -- Chu, Funderlic, and Golub -- Golub and Meurant -- Golub, Zhang, and Law -- Chandrasekaran, Golub, Gu, and Sayed -- Golub, Zhang, and Law --Golub and Wathen -- Golub, huang, Simon, and Tang -- Golub, Law, and Zhang -- Andersson, Elfving, and Golub -- Giladi, Golub, and Keller --Chandrasekaran, Golub, Gu, and Sayed -- Bablama, Calvetti, Golub, and Reichel -- T. Chan, Golub, and Mulet -- Calvetti, Golub, and Reichel --Chu, Funderlic, and Golub -- Golub, Zhang, and Law -- Benzi and Golub -- Calvetti, Golub, and Reichel -- Calvetti, Golub, and Reichel -- Golub, Hansen, and O’Leary -- Elhay, Gladwell, Golub, and Ram -- Chandrasekaran, Golub, Gu, and Sayed -- Golub and Ye -- Golub, Milanfar, and Varah -- Calvetti, Golub, Gragg, and Reichel --van der Vorst and Golub -- Golub, Murphy, and Wathen -- Golub and Ye -- Golub and Vanderstraeten -- Golub, Zhang, and Zha -- Golub, Solna, and van Dooren -- Golub, Sameh, and Sarin -- Golub, Nguyen, and Milanfar -- Golub, Nguyen, and Milanfar -- Golub and Melboe -- Golub, Wu, and Yuan -- Golub and Zhang -- Chu and Golub -- Concus, Golub, and Sun -- Golub, Greif, and Varah -- Golub and Yuan -- Elhay, Golub, and Ram -- Golub and Pereyra -- Golub and Greif -- Golub, Orchard, Greif, Bjornson, and Atkins -- Benzi, M. gander, and Golub -- bai, Golub, and Ng -- Alter and Golub -- Benzi and Golub -- Golub, Sima, Van Huffel -- Elad, Golub, and Milanfar -- Bai, Golub, and Pan -- Golub, Kamvar, Haveliwala -- Golub, Yuan, Plemmons, cecAlio -- Golub and Livne -- Golub, Vandebril, Barel, Mastronardi -- Boutry, Elad, Golub, Milanfar -- Golub, Tsaig, Elad, Milanfar -- Golub, Holz, and Law -- Bertaccini, Capizzano, Golub, and Possio -- Capizzano, Bertaccini, and Golub -- Golub, Greif, and Varah -- Benzi, Golub, and Liesen -- Bai, Golub, Lu, and Yin -- Cuyt, Golub, Milanfar, verdonk -- Alter and Golub -- Golub and Liao -- Botchev and Golub…

There will be no last book or paper.