Hubert Schwetlick
Department of Mathematics
Dresden University of Technology

Selected Articles and Reports

The labels correspond to the labels used in the List of Publications

[A63]
H. Schwetlick and K. Schreiber
Nonlinear Rayleigh Functionals
Linear Algebra Appl. In Press, 2010
doi: 10.1016/j.laa.2010.06.048
[pdf-file, 377 kbyte]

[A62]
H. Schwetlick and K. Schreiber
A Counterexample for Characterizing an Invariant Subspace of a Matrix
ETNA, Electronic Transactions on Numer. Anal., 31 (2008), pp. 295--305
[pdf-file, 156 kbyte]

Based on

[R18]
H. Schwetlick and K. Schreiber
A Counterexample for Characterizing an Invariant Subspace of a Matrix by a Block Singularity System
Preprint MATH-NM-07-2007, Techn. Univ. Dresden, December 2007
[pdf-file, 236 kbyte]

[A61]
K. Schreiber and H. Schwetlick
A Jacobi-Davidson like method for nonlinear eigenvalue problems based on singularity theory.
PAMM, Proc. Appl. Math. Mech., 7 (2007), 1020401--1020402
http://dx.doi.org/10.1002/pamm.200700527
[pdf-file, 87 kbyte]

Short version of

[R17]
H. Schwetlick and K. Schreiber
A primal-dual Jacobi-Davidson-like method for nonlinear eigenvalue problems
Internal Report ZIH-IR-0613, Techn. Univ. Dresden, Zentrum für Informationsdienste und Hochleistungsrechnen (ZIH), October 2006, pp. 1-20
Corrected version March 2007
[pdf-file, 458 kbyte]

[A60]
H. Schwetlick
Newton-Type Methods for Nonlinear Least Squares Using Restricted Second Order Information
In: Hans Georg Bock, Ekaterina Kostina, Hoang Xuan Phu, and Rolf Rannacher, editors,
Modeling, Simulation and Optimization of Complex Processes
Proc. International Conference on High Performance Scientific Computing, March 10-14, Hanoi, Vietnam
,
pp. 715-732, Springer, Berlin, 2004
[pdf-file, 193 kbyte]

[A59]
H. Schwetlick and U. Schnabel
Iterative computation of the smallest singular value and the corresponding singular vectors of a matrix
Linear Algebra Appl., 371 (2003), pp. 1-30
[pdf-file, 267 kbyte]

Revised and extended version of

[R14]
H. Schwetlick and U. Schnabel
Iterative computation of the smallest singular value and the corresponding singular vectors of a matrix
Preprint IOKOMO-06-97, Techn. Univ. Dresden, 1997
[ps-file, 679 kbyte]

[A58]
T. Schütze and H. Schwetlick
Bivariate free knot splines
BIT, 43 (2003), pp. 153-178
[pdf-file, 1494 kbyte]

Based on

[R16]
T. Schütze and H. Schwetlick
Bivariate free knot splines
Preprint MATH-NM-13-01, Techn. Univ. Dresden, 2001
[pdf-file, 1215 kbyte]

[A55]
H. Schwetlick and R. Lösche
A generalized Rayleigh quotient iteration for computing simple eigenvalues of nonnormal matrices
Z. Angew. Math. Mech., 80 (2000), pp. 9-25
[pdf-file, 370 kbyte]

Based on

[R15]
H. Schwetlick and R. Lösche
A generalized inverse iteration for computing simple eigenvalues of nonsymmetric matrices
Preprint IOKOMO-07-97, Techn. Univ. Dresden, 1997
[ps-file, 473kbyte]

[A54]
G. Pönisch, U. Schnabel, and H. Schwetlick
Computing multiple turning points by using simple extended systems and computational differentiation
Optimization Methods and Software, 10 (1999), pp. 639-668

Based on

[R13]
G. Pönisch, U. Schnabel, and H. Schwetlick
Computing multiple turning points
Preprint IOKOMO-04-96, Techn. Univ. Dresden, 1996
[ps-file, 317 kbyte]

[M2]
H. Schwetlick
Angewandte Mathematik heute: Vom mathematischen Modell zum Computerprogramms
In: Vorträge des 4. Dresdner Kolloquiums zur Mathematik und ihrer Didaktik am 23. Februar 1999
Techn. Univ. Dresden, Professur für Didaktik der Mathematik, 1999, pp. 13/01 - 13/13
[pdf-file, 239 kbyte]

[A53]
R. Lösche, H. Schwetlick, and G. Timmermann
A modified block Newton iteration for approximating an invariant subspace of a symmetric matrix
Linear Algebra Appl. 275/276 (1998), pp. 381-400
[pdf-file, 1.1 Mbyte]

Based on

[R12]
R. Lösche, H. Schwetlick, and G. Timmermann
A modified block Newton iteration for approximating an invariant subspace of a symmetric matrix
Preprint IOKOMO-03-96, Techn. Univ. Dresden, 1996
[ps-file, 593 kbyte]

[A52]
E. L. Allgower and H. Schwetlick
A general view of minimally extended systems for simple bifurcation points
Z. Angew. Math. Mech., 77 (1997), pp. 83-97
[ps-file, 295 kbyte]

[A51]
G. Pönisch, U. Schnabel, and H. Schwetlick
Computing multiple pitchfork bifurcation points
Computing, 59 (1997), pp. 209-222

Based on

[R10]
G. Pönisch, U. Schnabel, and H. Schwetlick
Computing multiple pitchfork bifurcation points
Preprint IOKOMO-09-95, Techn. Univ. Dresden, 1995
[ps-file, 245 kbyte]

[A50]
S. Schleiff and H. Schwetlick
Characterizastion and computation of period doubling points by minimally extended systems
Optimization Methods and Software 8 (1997), pp. 1-24.

Based on

[R11]
S. Schleiff and H. Schwetlick
Characterizastion and computation of period doubling points by minimally extended systems
Preprint MATH-NM-07-1996, Techn. Univ. Dresden, 1996
[ps-file, 722 kbyte]

[A49]
T. Schütze and H. Schwetlick
Constrained approximation by splines with free knots
BIT, 37 (1997), pp. 105-137
[ps-file, 452 kbyte]

[A45]
H. Schwetlick, G. Timmermann, and R. Lösche
Path following for large nonlinear equations by implicit block elimination based on recursive projections
In: J. Renegar, M. Shub, and S. Smale, editors, The Mathematics of Numerical Analysis. Proc. AMS-SIAM Summer Seminar Park City/Utah1996, volume 32 of Lectures in Applied Mathematics, pp. 715-732. American Mathematical Society, Providence, RI, 1996
[ps-file, 744 kbyte]

[A44]
H. Schwetlick and T. Schütze
Least squares approximation by splines with free knots
BIT, 35 (1995), pp. 361-384
[ps-file, 305 kbyte]

[A42]
H. Schwetlick and V. Kunert
Spline smoothing under constraints on derivatives
BIT, 33 (1993), 512-528

[A41]
H. Schwetlick
Numerical methods for least squares parameter estimation in linearly separated and related models
In: Proceedings of the International Workshop on Inverse Problems, Mitteilungen des Curt-Risch-Instituts für Dynamik, Schall- und Meßtechnik, CRI K-1/93, pp. 85-96. Universität Hannover, 1993
[ps-file, 180 kbyte]

[A40]
H. Schwetlick
Nonlinear parameter estimation: Models, criteria and algorithms
In: D. F. Griffiths and G. A. Watson, editors, Numerical Analysis 1991. Proceedings of the 14th Dundee Conference on Numerical Analysis, volume 260 of Pitman Research Notes in Mathematics Series, pp. 164-193. Longman Scientific & Technical, Harlow, Essex, 1992
[ps-file, 351 kbyte]

[A39]
H. Schwetlick
Nichtlineare Parameterschätzung: Modelle, Schätzkriterien und numerische Algorithmen
Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik, 2/91 (1991), pp. 13-51
[pdf-file, 368 kbyte]
[ps-file, 441 kbyte] (als booklet für A5-Broschüre formattiert, erfordert Duplex-Druck)

[A38]
A. Hoy and H. Schwetlick
Some superlinearly convergent methods for solving singular nonlinear equations
In :E. L. Allgower and K. Georg, editors, Computational Solution of Nonlinear Systems of Equations. Proc. SIAM-AMS Summer Seminar Ft. Collins/CO 1988, volume 26 of Lectures in Applied Mathematics, pp. 285-300. American Mathematical Society, Providence, RI, 1990

[A37]
H. Schwetlick
Nonstandard scaling matrices in trust region methods
In:E. L. Allgower and K. Georg, editors, Computational Solution of Nonlinear Systems of Equations. Proc. SIAM-AMS Summer Seminar Ft. Collins/CO 1988, volume 26 of Lectures in Applied Mathematics, pp. 587-604. American Mathematical Society, Providence, RI, 1990

[A36]
H. Schwetlick
Zur numerischen Behandlung nichtlinearer parameterabhängiger Gleichungen
Nova acta Leopoldina NF 61, 267 (1989), pp. 107-136

[A35]
H. Schwetlick and V. Tiller.
Nonstandard scaling matrices for trust region Gauss-Newton methods.
SIAM J. Sci. Statist. Comput., 10 (1989), pp. 654-670

[A34]
R. Wolke and H. Schwetlick
Iteratively reweighted least squares: Algorithms, convergence, and numerical comparisons
SIAM J. Sci. Statist. Comput., 9 (1988), pp. 907-921

[A30]
R. Menzel und H. Schwetlick
Parametrization via Secant Length and Application to Path Following
Numer. Math., 47 (1985), pp. 401-412
[pdf-file, 817 kbyte]

[A22]
G. Pönisch und H. Schwetlick
Ein lokal üuberlinear konvergentes Verfahren zur Bestimmung von Rückkehrpunkten implizit definierter Raumkurven
Numer. Math., 38 (1982), pp. 455-466
[pdf-file, 754 kbyte]

[A19]
R. Menzel und H. Schwetlick
Zur Lösung parameterabhängiger nichtlinearer Gleichungen mit singulären Jacobi-Matrizen
Numer. Math., 30 (1978), pp. 65-79
[pdf-file, 1.2 Mbyte]