Prof. Martin H. Gutknecht
(Retired from ETH Zurich, but still active. Unfortunately no longer as young as on the picture of 1997!)
Seminar for Applied Mathematics
ETH Zurich
HG G50.1
CH8092 Zurich
Switzerland
My Last Courses:
My Last Research Papers:
 Revisiting (k,l)step methods [May 2014/Aug. 2014/Numer. Algor. 69,
455469 (electr. Sep. 2014, on paper June 2015)]
(preprint in my color style,
final version: NUMA)
 Deflated and augmented Krylov subspace methods:
A framework for deflated BiCG and related solvers
[May 2013/Mar. 2014/Sep. 2014; SIAM J. Matrix Anal. Appl. 35, 14441466 (2014).]
(rev. 1 in my color style;
final version:
SIMAX;
Supplementary Material)
 A framework for deflated and augmented Krylov subspace methods
(with André Gaul, Jörg Liesen, and Reinhard Nabben)
[June 2012 / Jan. 2013; SIAM J. Matrix Anal. Appl. 34, 495518 (2013).]
(arXiv (June 2012),
final version:
SIMAX)
First report version:
Deflated and augmented Krylov subspace methods: Basic facts and a breakdownfree
deflated MINRES (with André Gaul, Jörg Liesen, and Reinhard Nabben)
[Jan. 2011; Preprint 759, DFG Research Center MATHEON, TU Berlin]
(Preprint TUB)
 Spectral deflation in Krylov solvers: A theory of coordinate space based methods.
[Nov. 2011/Apr. 2012; Research Report No. 201171, SAM, ETH;
Electr. Trans. Numer. Anal. 39, 156185 (2012).]
(Res.Rep.SAM,
cor.print,
ETNA)
 Eigenvalue computations based on IDR (with JensPeter M. Zemke)
[May 2010 / Dec. 2012; SIAM J. Matrix Anal. Appl. 34, 283311 (2013).]
(Final version:
SIMAX)
Original extended version:
[May 2010;
Research Report No. 201013, SAM, ETH;
Bericht Nr. 145, INS, TU HamburgHarburg]
(Res.Rep.SAM,
Bericht TUHH)
[July 2010/Mar. 2012; SIAM J. Matrix Anal. Appl.]
 From qd to LR and QR, or, how were the qd and LR algorithms discovered?
(with Beresford N. Parlett)[Aug. 2009/Dec. 2009;
IMA J. Numer. Anal. 31, 741754 (2011); first publ. online May 27, 2010]
(submitted ms.,
link to IMAJNA)
 IDR explained
[Dec. 2008/Oct. 2009; Electr. Trans. Numer. Anal. 36, 126148 (2010)]
(Final version from ETNA;
my color style)
 How to make Simpler GMRES and GCR more stable
(with Pavel Jiranek and Miroslav Rozloznik) [Oct. 2007/Aug. 2008;
SIAM J. Matrix Anal. Appl. 30, 14831499 (2008)]
(Final version:
SIMAX)
 Numerical analysis in Zurich  50 years ago
[Mar. 2007; Zurich Intelligencer, SpringerVerlag, July 2007]
(Final proof)
 The block grade of a block Krylov space (with Th. Schmelzer)
[July 2006/July 2008; Linear Algebra Appl. 430, 174185 (2009)]
(Final version:
LAA )
 A brief introduction to Krylov space methods for solving
linear systems
[Feb. 2006; Frontiers of Computational Science  Proceedings of the
International Symposium on Frontiers of Computational Science 2005
(Y. Kaneda, H. Kawamura, and M. Sasai, eds.), pages 5362,
SpringerVerlag, Berlin Heidelberg, Mar. 2007]
(Preprint)
 Updating the QR decomposition of block tridiagonal and block
Hessenberg matrices (with Th. Schmelzer)
[Nov. 2005, rev. Mar. 2007, online Apr. 2007; Appl. Num. Math. 58,
871883 (2008)]
(Final version:
APNUM)
 Block Krylov space methods for linear systems with
multiple righthand sides: an introduction
[Aug. 2005; in: Modern Mathematical Models, Methods and Algorithms for
Real World Systems (A.H. Siddiqi, I.S. Duff, and O. Christensen, eds.),
pages 420447, Anamaya Publishers, New Delhi, India, 2007]
(Preprint)
[The published version has been retyped by Anayama Publishers and contains
hundreds of misprints!]
 A General framework for recursions for Krylov space solvers
[Aug. 2005]
(Preprint)
 A QRdecomposition of block tridiagonal matrices generated by the
block Lanczos process (with Th. Schmelzer)
[May 2005; Proceedings IMACS World Congress 2005 (on CD only)]
(Final version)
 A framework for generalized conjugate gradient methods 
with special emphasis on contributions by Rüdiger Weiss
(with M. Rozloznik)
[Dec. 2000; rev. Mar. 2001; Appl. Numer. Math. 41, 722 (2002)]
(Final version:
APNUM)
 Variations of Zhang's Lanczostype product method
(with S. Röllin)
[Dec. 2000; rev. Mar. 2001; Appl. Numer. Math. 41, 119133 (2002)]
(Preprint [PostScript compressed])
 The Chebyshev iteration revisited
[Dec. 2000; rev. Apr. 2001; Parallel Comput. 28, 263283 (2002)]
(Preprint [PostScript compressed],
final version:
Parallel Comput.)
 By how much can residual minimization accelerate the convergence
of orthogonal residual methods? (with M. Rozloznik)
[Jul. 2000; rev. May 2001; Numer. Algor. 27, 189213 (2001)]]
(Preprint [PostScript compressed])
 A matrix interpretation of the extended Euclidean algorithm
[Mar. 2000; rev. May 2000; in: Structured Matrices in
Mathematics, Computer Science, and Engineering, Vol. 1
(V. Olshevsky, ed.), pages 5370, Contemporary Mathematics, Vol. 280,
American Mathematical Society, 2001]
(Preprint [PostScript compressed])
 On Lanczostype methods for Wilson fermions [Nov. 1999; revised,
April 2000; in: Numerical Challenges in Lattice Quantum
Chromodynamics (A. Frommer et al., eds.), LNCSE, Vol. 15, Springer, 2000]
(Preprint [PostScript compressed])
 Residual smoothing techniques: do they improve the limiting accuracy of
iterative solvers? (with M. Rozloznik)
[Oct. 1999/May 2000; BIT 41, 86114 (2001)]
(Preprint [PostScript compressed];
final:
BIT
)
 Theodorsen's integral equation
[Sep. 1999; Encyclopaedia of Mathematics, Supplement III (M. Hazewinkel, ed.),
pages 401402,Kluwer, 2001]
(Preprint [PostScript compressed])
 Accuracy of two threeterm and three twoterm recurrences for Krylov
space solvers (with Z. Strakos)
[revised, Oct. 1999; SIAM J. Matrix Anal. 22, 213229(2000)]
(Preprint [PostScript compressed];
final:
SIAM)
 Lookahead procedures for Lanczostype product methods based on threeterm
Lanczos recurrences (with K.J. Ressel) [revised, Jul. 1999;
SIAM J. Matrix Anal. 21, 10511078 (2000)]
(Preprint [PostScript compressed];
final:
SIAM)
Older Preprints or Reprints Available:
 Copper Mountain Conference on Iterative Methods, 1990:
The unsymmetric Lanczos algorithms and their relations to Padé approximation,
continued fractions, and the qd algorithm
( Sections 16,
Section 7,
Errata)
 Conference on the History of Scientific and Numeric Computation, 1987:
The pioneer days of scientific computing in Switzerland
(pdf)
Some Recent Talks:
 "How accurate is Gauss quadrature with indefinite or complex weight function?"
Talk presented at "The Third International Workshop on Matrix Computation" organized online by Lanzhou University, Lanzhou, PR China (Apr. 1519, 2022).
(PDF in beamer.sty)
[Related: handwritten slides on Padé forms.
(PDF of scan)]
 "New insight on how Rutishauser discovered the qd algorithm"
(Further extended version of "How Rutishauser may have found the qd and LR algorithms, the forerunners of QR")
Talk presented at "The Third International Workshop on Matrix Computation" organized online by Lanzhou University, Lanzhou, PR China (Apr. 1519, 2022).
( PDF in beamer.sty)
 "Spectral deflation in Krylov solvers" or
" Deflation based preconditioning of linear systems of equations"
Talk presented first at the International Conference on Numerical Algebra
and Scientific Computinng (NASC10), Beijing (2327 October 2010).
(last version, PDF in beamer.sty)
 "From qd to LR and QR, or, How were the qd and LR algorithms
discovered?"
(Extended version of "How Rutishauser may have found the qd and LR algorithms,
the forerunners of QR")
Talk presented at the Computational Science Workshop "Sparse Matrix Solvers and
Preconditioning", Keio University, Hiyoshi, Tokio, Japan (Mar. 29, 2010).
(PDF in beamer.sty)
 "The kernel structure of rectangular Hankel and Toeplitz matrices"
Talk presented at the "3rd International Conference on Structured Matrices and Tensors",
Hong Kong, PR China (1922 January 2010).
(PDF in beamer.sty)
 "IDR  a brief introduction"
Talk presented in the Minisymposium "Induced Dimension Reduction (IDR) methods:
a family of efficient Krylov solvers" of the SIAM Conference on Applied Linear
Algebra (LA09), Monterey, CA, USA (Oct 27, 2009).
(PDF in beamer.sty)
 "Block and Band Lanczos Algorithms: a Review of Options"
Talk presented at the Autumn School "Future Developments in Model Order Reduction",
Terschelling, The Netherlands (Sep 22, 2009).
(PDF in beamer.sty)
 "How Rutishauser may have found the qd and LR algorithms,
the forerunners of QR"
Talk presented in the Minisymposium "The QR Algorithm: 50 years later,
its genesis by John Francis, and subsequent developments" of the
23rd Biennial Conference on Numerical Analysis, U Strathclyde, Glasgow, Scotland
(2326 June 2009).
(PDF in beamer.sty)
 "IDR in Variations"
Talk presented at TU Berlin (Dec 16, 2008), WIAS Berlin (Jan 12, 2009),
TU Freiberg (Jan 16, 2009), TU Chemnitz (Jan 20, 2009), TU HamburgHarburg
(Jan 28, 2009).
(PDF in beamer.sty)
 "Modified Moments for Indefinite Weight Functions"
(a Tribute to a Fruitful Collaboration with Gene H. Golub)
My contribution to " Remembering Gene Golub Around the World",
presented in Leuven, February 29, 2008.
(
1. PDF handout in beamer.sty;
2. scanned slides from talk presented at Richard S. Varga's 60th birthday
meeting, Kent, OH, Mar. 31, 1989)
 "Krylov Space Solvers"
An introductory lecture stressing basic ideas; not a survey of methods.
Talk given at International Symposium on Frontiers of Computational Science,
Dec. 1213, Nagoya, 2005.
(PDF in beamer.sty)
 "Block Krylov Space Solvers: a Survey"
A survey of selected work on block Krylov methods.
Talk given at Nagoya University, Dec. 8, 2005.
(PDF in beamer.sty)
 "Block Krylov Space Methods for Linear Systems With
Multiple Righthand Sides"
Basic aspects of block Krylov methods; effects of deflation in block GMRES
and in symmetric block Lanczos.
Talk given at the Householder Symposium XVI, May 58, 2005,
Seven Springs Mountain, PA, and at the
Joint Workshop on Computational Chemistry and Numerical Analysis (CCNA2005),
Dec. 56, 2005, Tokyo.
(PDF in beamer.sty)
Some Older Talks:
 Phoenix, AZ, USA (Jan. 89), Umhlange Rocks, SA (Jul. 89), Copper Mtn., CO, USA (Apr. 90), ...:
"The unsymmetric Lanczos algorithms and their relations to Padé
approximation, continued fractions, and the qd algorithm"
(scans/PDF),
 Richard S. Varga's 60th birthday meeting, Kent, OH, Mar. 31, 1989:
"Modified Moments for Indefinite Weight Functions"
(scans/PDF)
 Householder Symposium 1990, Tylosand, Sweden:
"A Completed Theory of the Unsymmetric Lanczos Process and Related
Algorithms"
(scans/PDF)
 50th Anniversary of the Institute/Seminar for Applied Mathematics, ETH Zurich (Nov. 18, 1998):
"Contributions to Numerical Analysis in the 1950ies"
(PostScript,
compressed)
 "The Conjugate Gradient Method"
(PostScript,
compressed,
two color figures:
CGFig.ps,
SteepDescFig.ps)
 "LanczosType Solvers for NonHermitian Linear Systems"
(PostScript,
compressed)
Personal Information: (partly outdated)
Former Functions:
Address information for former members of the SPS section of CSCS/SCSC
Present university positions of some former IPS/SCSC students and postdocs
Mathematical Genealogy:
(from
Gerard L.G. Sleijpen and
The Mathematics Genealogy Project)
 C. Felix (Christian) Klein, Bonn 1868
 C. L. Ferdinand (Carl Louis) Lindemann, ErlangenNürnberg 1873
 David Hilbert, Königsberg 1885
 Erhard Schmidt, Göttingen 1905, and
Ludwig Bieberbach, Göttingen 1910
 Heinz Hopf, Berlin 1925
 Eduard Stiefel, Zürich 1935
 Peter Henrici, Zürich 1953
 Martin H. Gutknecht, Zürich 1973

Latsis Symposium 2002 on Iterative Solvers for Large Linear Systems
("CG50GG70")
In 1952, M. Hestenes and E. Stiefel published their seminal paper
``Methods of conjugate gradients for solving linear systems''
in J. Research Nat. Bur. Standards 49 (1952), 409436''. This conference,
which was held at ETH Zurich February 1821, 2002,
had the purpose to commemorate this event, review the early and later
developments, survey the tremendous impact of the CG paper, and discuss
current research in the area of Krylov space methods and their
preconditioning. Simultaneously, it hosted a celebration of Professor
Gene Golub's 70th birthday.
Transcribed remarks, lecture notes, and slides from the presentations
of Todd, Hochstrasser, and Bauer
Some pictures of the conference
50 years CG
celebration at NIST
Dianne O'Leary's article in the NIST centennial publication
A Century of Excellence in Measurements, Standards, and Technology,
A Chronicle of Selected NBS/NIST Publications, 19012000
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