Schriftenverzeichnis
- Mayer, G.: Linearisierte Theorie von Schiffswellen und
Wellenwiderstand bei ungleichförmiger Anströmung.
Dissertation, Universität Karlsruhe, Karlsruhe, 1982.
- Mayer, G.: On the Convergence of Powers of Interval Matrices.
Linear Algebra Appl. 58, 201-216 (1984)
- Mayer, G.: Schiffswellen bei tiefenabhängiger
Anströmung.
Z. angew. Math. Mech. 64, T210-T212
(1984).
- Mayer, G.: On the Convergence of the Neumann Series in Interval
Analysis.
Linear Algebra Appl. 65, 63-70 (1985).
- Mayer, G.: On the Convergence of Powers of Interval Matrices
(2).
Numer. Math. 46, 69-83 (1985).
- Mayer, G.: Enclosing the Solution Set of Linear Systems with
Inaccurate Data by Iterative Methods Based on Incomplete
LU--Decompositions.
Computing 35, 189-206 (1985).
- Mayer, G.: Über die Konvergenz von
Intervallmatrizenpotenzen.
Z. angew. Math. Mech. 65, T393-T394
(1985).
- Mayer, G.: Reguläre Zerlegungen und der Satz von Stein und
Rosenberg für Intervallmatrizen.
Habilitationsschrift,
Universität Karlsruhe, Karlsruhe, 1986.
- Mayer, G.: On a Theorem of Stein-Rosenberg Type in Interval
Analysis.
Numer. Math. 50, 17-26 (1986).
- Mayer, G.: Über Iterationsverfahren zur
Lösungseinschließung linearer Gleichungssysteme mit
ungenauen Eingangsdaten.
Z. angew. Math. Mech. 66, T417-T419
(1986).
- Mayer, G.: On the Asymptotic Convergence Factor of the Total
Step Method in Interval Computation.
Linear Algebra Appl. 85,
153-164 (1987).
- Mayer, G.: Comparison Theorems for Iterative Methods Based on
Strong Splittings.
SIAM J. Numer. Anal. 24, 215-227 (1987).
- Mayer, G.: On the Speed of Convergence of the Total Step Method
in Interval Computations.
In Ortiz, E.L. (ed.): Numerical
Approximation of Partial Differential Equations. Mathematics
Studies Vol. 133. North-Holland, Amsterdam, 181-189 (1987).
- Mayer, G.: ÜUber den asymptotischen Konvergenzfaktor des
Einzelschrittverfahrens in der Intervallrechnung.
Z. angew.
Math. Mech. 67, T490-T492 (1987).
- Mayer, G.: Über mathematische Modelle zur Penetration
starrer Stäbe in Sand.
Interner Bericht, Universität
Karlsruhe, Karlsruhe, 1987.
- Mayer, G.: Enclosing the Solutions of Systems of Linear
Equations by Interval Iterative Processes.
In Kulisch, U.,
Stetter, H.J. (eds.): Scientific Computation with Automatic Result
Verification. Computing Suppl. 6, 47-58 (1988).
- Mayer, G.: On the Speed of Convergence of Some Iterative
Processes.
In Greenspan, D., R\'{o}sza, P. (eds.): Numerical
Methods. Colloquia Mathematica Societatis J\'{a}nos Bolyai, 50. North
Holland, Amsterdam, 207-228 (1988).
- Mayer, G.: Zur Lösungseinschließung bei nichtlinearen
Gleichungssystemen.
Z. angew. Math. Mech. 68, T499-T500
(1988).
- Frommer, A., Mayer, G.: Parallel Interval Multisplittings.
Numer. Math. 56, 255-267 (1989).
- Frommer, A., Mayer, G.: Convergence of Relaxed Parallel
Multisplitting Methods.
Linear Algebra Appl. 119, 141-152
(1989).
- Frommer, A., Mayer, G.: Safe Bounds for the Solutions of
Nonlinear Problems Using a Parallel Multisplitting Method.
Computing 42, 171-186 (1989).
- Frommer, A., Mayer, G.: Zur Lösungseinschließung bei
linearen Gleichungssystemen auf einem Parallelrechner.
Z. angew.
Math. Mech. 69, T102-T103 (1989).
- Mayer, G.: On Newton-like Methods to Enclose Solutions of
Nonlinear Equations.
Apl. Mat. 34, 67-84 (1989).
- Mayer, G.: Grundbegriffe der Intervallrechnung.
In Kulisch,
U. (Hrsg.): Wissenschaftliches Rechnen mit Ergebnisverifikation.
Akademie-Verlag, Berlin 58, 101-118 (1989).
Auch: Vieweg-Verlag,
Wiesbaden, 101-118 (1989).
- Block, U., Frommer, A., Mayer, G.: Block Colouring Schemes for
the SOR--Method on Local Memory Parallel Computers.
Parallel
Comput.14, 61-75 (1990).
- Block, U., Frommer, A., Mayer, G.: Block--Colouring Schemes for
the SOR Method on Parallel Computers.
Methods Oper. Res. 62,
447-449 (1990).
- Block, U., Frommer, A., Mayer, G.: Block Iterative Methods for
Binary Tree Computers.
Methods Oper. Res. 62, 451-453
(1990).
- Frommer, A., Mayer, G.: On the R-Order of Newton-like Methods
for Enclosing Solutions of Nonlinear Equations.
SIAM J. Numer.
Anal. 27, 105-116 (1990).
- Frommer, A., Mayer, G.: Efficient Methods for Enclosing
Solutions of Systems of Nonlinear Equations.
Computing 44,
221-235 (1990).
- Frommer, A., Mayer, G.: Theoretische und praktische Ergebnisse
zu Multisplitting-Verfahren auf Parallelrechnern.
Z. angew.
Math. Mech. 70, T600-T602 (1990).
- Frommer, A., Mayer, G.: Efficient Modifications of the Interval
Newton Method.
In Ullrich, C. (ed.): Contributions to Computer
Arithmetic and Self-Validating Numerical Methods. IMACS Annals on
Computing and Applied Mathematics, 7. Baltzer, Basel, 213-227
(1990).
- Mayer, G., Frommer, A.: A Multisplitting Method for Verification
and Enclosure on a Parallel Computer.
In Ullrich, C. (ed.):
Contributions to Computer Arithmetic and Self-Validating Numerical
Methods. IMACS Annals on Computing and Applied Mathematics, 7.
Baltzer, Basel, 483-497 (1990).
- Mayer, G., Frommer, A.: Über die R-Ordnung bei
Newton-ähnlichen Iterationsverfahren.
Z. angew. Math. Mech.
70, T558-T559 (1990).
- Block, U., Frommer, A., Mayer, G.: SOR-ähnliche Verfahren
auf einem Prototypen des TX3.
Arbeitspapiere der GMD 523 (1991).
- Block, U., Frommer, A., Mayer, G.: Farbschemata für das
SOR-Verfahren und Beispiele auf dem Prototypen des TX3.
Arbeitspapiere der GMD 523 (1991).
- Frommer, A., Mayer, G.: Iterationsverfahren für lineare
Gleichungssysteme auf Parallelrechnern.
Z. angew. Math. Mech.
71, T799-T801 (1991).
- Mayer, G.: Old and New Aspects on the Interval Gaussian
Algorithm.
In Kaucher, E., Markov, S.M., Mayer, G. (eds.):
Computer Arithmetic, Scientific Computation and Mathematical
Modelling. IMACS Annals on Computing and Applied Mathematics, 12.
Baltzer, Basel, 329-349 (1991).
- Frommer, A., Mayer, G.: On the Theory and Practice of
Multisplitting Methods in Parallel Computation.
Computing 49,
63-74 (1992).
- Mayer, G.: Some Remarks on Two Interval-Arithmetic Modifications
of the Newton Method.
Computing 48, 125-128 (1992).
- Mayer, G.: Enclosures for Eigenvalues and Eigenvectors.
In
Atanassova, L., Herzberger, J. (eds.): Computer Arithmetic and
Enclosure Methods. Elsevier, Amsterdam, 49-67 (1992).
- Alefeld, G., Mayer, G.: The Cholesky Method for Interval Data.
Linear Algebra Appl. 194, 161-182 (1993).
- Foerster, N., Frommer, A., Mayer, G.: Inexakte Newton-Verfahren
auf Supercomputern.
Z. angew. Math. Mech. 73, T950-T953
(1993).
- Frommer, A., Mayer, G.: A New Criterion to Guarantee the
Feasibility of the Interval Gaussian Algorithm.
SIAM J. Matrix
Anal. Appl. 14, 408-419 (1993).
- Frommer, A., Mayer, G.: Two-Stage Interval Iterative Methods.
In Albrecht, R., Alefeld, G., Stetter, H. J. (eds.): Validation
Numerics. Theory and Applications. Computing Suppl. 9, 45-65
(1993).
- Frommer, A., Mayer, G.: Linear Systems with Omega-Diagonally
Dominant Matrices and Related Ones.
Linear Algebra Appl. 186,
165-181 (1993).
- Mayer, G.: Taylor-Verfahren für das algebraische
Eigenwertproblem.
Z. angew. Math. Mech. 73, T 857-T 860
(1993).
- Mayer, G., Pieper, L.: A Necessary and Sufficient Criterion to
Guarantee the Feasibility of the Interval Gaussian Algorithm for a
Class of Matrices.
Appl. Math. 38, 205-220 (1993).
- Alefeld, G., Gienger, A., Mayer, G.: Numerical Validation for an
Inverse Matrix Eigenvalue Problem.
Computing 53, 311 - 322
(1994).
- Alefeld, G., Mayer, G.: A Computer-Aided Existence and
Uniqueness Proof for an Inverse Matrix Eigenvalue Problem.
Intern. J. Interval Computations 1994/1, 4-27 (1994). Auch als
Preprint Nr. 93/2 des IWRMM, Universität Karlsruhe, 1993,
erschienen.
- Alefeld, G., Mayer, G.: Symmetric Interval Systems.
In:
Jiang Er-xiong (ed.), Proceedings of the '92 Shanghai International
Numerical Algebra and its Applications Conference, Chinese Science
and Technology Press, 7-12 (1994).
- Alefeld, G., Mayer, G.: Über eine Intervallversion des
Cholesky-Verfahrens.
Z. angew. Math. Mech. 74, T679-T681
(1994).
- Mayer, G.: A Unified Approach to Enclosure Methods for
Eigenpairs.
Z. angew. Math. Mech. 74, 115-128 (1994).
- Mayer, G.: Ergebnisverifikation beim algebraischen
Eigenwertproblem.
In Chatterji, S. D., Fuchssteiner, B.,
Kulisch, U., Liedl, R. (Hrsg.): Jahrbuch Überblicke Mathematik
1994. Vieweg, Braunschweig, 111-130 (1994).
- Mayer, G.: Result Verification for Eigenvectors and Eigenvalues.
In Herzberger, J. (ed.): Topics in Validated Computations.
Elsevier, Amsterdam, 209-276 (1994).
- Alefeld, G., Lenhardt, I., Mayer, G.: Einfluß der
Gewichte bei überlappenden Multisplitting-Verfahren für
Bandmatrizen.
Z. angew. Math. Mech. 75, SII, S609 - S610
(1995).
- Alefeld, G., Mayer, G.: On the Symmetric and Unsymmetric
Solution Set of Interval Systems.
SIAM J. Matrix Anal. Appl. 16,
1223-1240 (1995).
- Alefeld, G., Mayer, G.: Einschließungsverfahren.
In:
Herzberger, J. (Hrsg.): Wissenschaftliches Rechnen. Eine
Einführung in das Scientific Computing. Akademie Verlag,
Berlin, 155-186 (1995).
- Foerster, H., Frommer, A., Mayer, G.: Inexact m-Step Newton
Methods on a Vector Supercomputer.
J. Comp. Appl. Math. 58,
237-253 (1995).
- Kreinovich, V., Mayer, G.: Towards the Future of Interval
Computations.
Reliable Computing 1 (3), 209-214 (1995).
- Mayer, G.: Epsilon-Inflation in Verification Algorithms.
J.
Comp. Appl. Math. 60, 147-169 (1995).
- Mayer, G.: On a Unified Representation of Some Interval Analytic
Algorithms.
Rostock. Math. Kolloq. 49, 75-88 (1995).
- Mayer, G.: Über ein Prinzip in der Verifikationsnumerik.
Z. angew. Math. Mech. 75, SII, S 545 - S 546 (1995).
- Alefeld, G., Kreinovich, V., Mayer, G.: The Shape of the
Symmetric Solution Set.
In Kearfott, R. B., Kreinovich, V.
(eds.): Applications of Interval Computations. Applied Optimization
3, Kluwer, Boston, 61-79 (1996).
- Alefeld, G., Kreinovich, V., Mayer, G.: Symmetric Linear Systems
with Perturbed Input Data.
In Alefeld, G., Herzberger, J.
(eds.): Numerical Methods and Error Bounds. Akademie Verlag, Berlin,
16-22 (1996).
- Alefeld, G., Lenhardt, I., Mayer, G.: On Multisplitting Methods
for Linear Systems of Equations.
In: Alefeld, G., Mahrenholz,
O., Mennicken, R. (eds.): ICIAM/GAMM 95. Numerical Analysis,
Scientific Computing, Computer Science. Hamburg, July 3-7, 1995. Z.
angew. Math. Mech. 76, Suppl. 1, 111-114 (1996).
- Alefeld, G., Mayer, G.: On the Solution Set of Symmetric
Interval Systems.
In: Mahrenholz, O., Marti, K., Mennicken, R.
(eds.): ICIAM/GAMM 95. Applied Stochastics and Optimization.
Hamburg, July 3-7, 1995. Z. angew. Math. Mech. 76, Suppl. 3, 259-262
(1996).
- Mayer, G.: Assessing the Accuracy and Reliability of Numerical
Solutions.
In: Alefeld, G., Mahrenholz, O., Mennicken, R.
(eds.): ICIAM/GAMM 95. Numerical Analysis, Scientific Computing,
Computer Science. Hamburg, July 3-7, 1995. Z. angew. Math. Mech. 76,
Suppl. 1, 195-198 (1996).
- Mayer, G.: Success in Epsilon-Inflation.
In: Alefeld, G.,
Frommer, A., Lang, B. (eds.): Scientific Computing and Validated
Numerics. Akademie Verlag, Berlin, 98-104 (1996).
- Alefeld, G., Koshelev, M., Mayer, G.: Why it is Computationally
Harder to Reconstruct the Past than to Predict the Future.
International J. Theor. Physics 36, 1709-1715 (1997).
- Alefeld, G., Koshelev, M., Mayer, G.: Fixed Future and Uncertain
Past: Theorems Explain why it is Often More Difficult to Reconstruct
the Past than to Predict the Future.
In Jamshidi, M., Lumia, R.,
Tunstel, E., White, B., Malone J., Sakimoto, P. (eds.): NASA
University Research Center Technical Advances on Education,
Aeronautics, Space, Autonomy, Earth and Environment. Vol. 1:
Proceedings of the NASA University Research Center Technical
Conference. February 16-19, 1997, Albuqerque, New Mexico. ACE Center
Press, Albuquerque, 23-27 (1997).
- Alefeld, G., Kreinovich, V., Mayer, G.: On the Shape of the
Symmetric, Persymmetric, and Skew-Symmetric Solution Set.
SIAM
J. Matrix Anal. Appl. 18, 693-705 (1997).
- Alefeld, G., Lenhardt, I., Mayer, G.: On Multisplitting Methods
for Band Matrices.
Numer. Math. 75, 267-292 (1997).
- Kreinovich, V., Starks, S., Mayer, G., : On a Theoretical
Justification of the Choice of Epsilon-Inflation in PASCAL-XSC.
Reliable Computing 3, 437-445 (1997).
- Mayer, G.: Quantitative Results on Epsilon-Inflation.
Z.
angew. Math. Mech. 77, Suppl. 2, S617-S618 (1997).
- Alefeld, G., Kreinovich, V., Mayer, G.: The Shape of the
Solution Set for Interval Systems with Dependent Coefficients.
Math. Nachr. 192, 23-26 (1998).
- Mayer, G., Rohn, J.: On the Applicability of the Interval
Gaussian Algorithm.
Reliable Computing 4, 205-222 (1998).
- Mayer, G.: Epsilon-Inflation with Contractive Interval
Functions.
Applications of Mathematics 43, 241-254 (1998).
- Alefeld, G., Hoffmann, R., Mayer, G.: Verification Algorithms
for Generalized Singular Values.
Math. Nachr. 208, 5-29
(1999).
- Alefeld, G., Mayer, G.: Interval Analysis: Theory and
Applications.
J. Comp. Appl. Math. 121, 421-464 (2000), Special
Issue: Wuytack, L., Wimp, J. (eds.): Numerical Analysis in the 20th
Century, Vol. I. Approximation Theory.
- Mayer, G.: Beiträge zur Intervallrechnung.
In: Walz, G.
(Hrsg.): Lexikon der Mathematik. Spektrum-Verlag, Mannheim
(2000).
- Alefeld, G., Kreinovich, V., Mayer, G.: Modifications of the
Oettli-Prager Theorem with Application to the Algebraic Eigenvalue
Problem.
In: Alefeld, G., Rohn, J., Rump, S. M., Yamamoto, T.
(eds.): Symbolic Algebraic Methods and Verification Methods - Theory
and Applications. Springer, Wien, 11-20 (2001).
- Alefeld, G., Kreinovich, V., Mayer, G., Huth, M.: A Comment on
the Shape of the Solution Set for Systems of Interval Linear
Equations with Dependent Coefficients.
Reliable Computing, 7,
275-277 (2001).
- Alefeld, G., Mayer, G.: The Gaussian Algorithm for Linear
Systems with Interval Data.
In Carlson, D., Johnson, C. R., Lay,
D. C., Porter, A. D. (eds.): Linear Algebra Gems: Assets for the
Undergraduate Mathematics. The Mathematical Association of America.
MAA Notes #59, 2001, pp. 197-204.
- Mayer, G.: A New Way to Describe the Symmetric Solution Set
S_sym of Linear Interval Systems.
In Alefeld, G., Chen, X.:
Topics in Numerical Analysis with Special Emphasis on Nonlinear
Problems. Computing Supplementum 15, 151-163 (2001).
- Mayer, G., Warnke, I.: On the Shape of the Fixed Points of
[f]([x]) = [A] [x] + [b] .
In: Alefeld, G., Rohn, J., Rump, S.
M., Yamamoto, T. (eds.): Symbolic Algebraic Methods and Verification
Methods - Theory and Applications. Springer, Wien, 153-162
(2001).
- Mayer, G., Warnke, I.: On the Limit of the Total Step Method in
Interval Analysis.
In: Facius, A., Lohner, R., Kulisch, U.
(eds.): Perspectives of Enclosure Methods. Springer, Wien, 157-172
(2001).
- Alefeld, G., Kreinovich, V., Mayer, G.: On the Solution Sets of
Particular Classes of Linear Systems.
J. Comp. Appl. Math. 152,
1-15 (2003).
- Alefeld, G., Kreinovich, V., Mayer, G.: On Symmetric Solution
Sets.
In: Herzberger, J. (ed.): Inclusion Methods for Nonlinear
Problems. With Applications in Engineering, Economics and Physics.
Computing Supplementum 16, 1-22 (2003).
- Mayer, G., Warnke, I.: On the Fixed Points of the Interval
Function [f]([x]) = [A] [x] + [b] .
Linear Algebra Appl. 363,
201-216 (2003).
- Alefeld, G., Mayer, G.: On Singular Interval Systems.
In
Alt, R., Frommer, A., Kearfott, R.B., Luther, W. (eds.): Numerical
software with result verification (Platforms, algorithms,
applications in engineering, physics and economics), Lecture Notes
in Computer Science, Springer, Berlin, 191-197 (2004).
- Arndt, H.-R., Mayer, G.: On the Semi-Convergence of Interval
Matrices.
Linear Algebra Appl. 393, 15-37 (2004).
- Alefeld, G., Mayer, G.: Enclosing Solutions of Singular Systems
Iteratively.
Reliable Computing 11, 165-190 (2005).
- Arndt, H.-R., Mayer, G.: On the Solutions of the Interval System
[x]=[A][x]+[b].
Reliable Computing 11, 87-103 (2005).
- Arndt, H.-R., Mayer, G.: New Criteria for the Semi-Convergence
of Interval Matrices.
SIAM J. Matrix Anal. Appl. 27 (3),
689-711 (2005).
- Kosheleva, O., Kreinovich, V., Mayer, G., Nguyen, H.T.:
Computing the Cube of an Interval Matrix is NP-Hard.
Proceedings
of the 2005 ACM Symposium on Applied Computing (SAC 2005), Vol. 2 of
2 (2005) 1449-1453.
- Mayer, G.: A Contribution to the Feasibility of the Interval
Gaussian Algorithm.
Reliable Computing 12 (2), 79-98
(2006).
- Mayer, G.: On Regular and Singular Interval Systems.
J.
Comp. Appl. Math. 199 (2), 220-228 (2007).
- Mayer, G.: On the Interval Gaussian Algorithm.
In Luther,
W., Otten, W. (eds.): IEEE-Proceedings of SCAN 2006, 12th GAMM-IMACS
International Symposium on Scientific Computing, Computer Arithmetic
and Validated Numerics, Duisburg, Germany, September 26-29, 2006,
IEEE Computer Society, Washington, DC, ISBN 0-7695-2821-X (2007) CD,
8 Seiten.
- Ceberio, M., Kreinovich, V., Mayer, G.: For Complex Intervals,
Exact Range Computation is NP-Hard Even for Single Use Expressions
(Even for the Product).
In Y. Cho, R.L. Wainwright, H. Haddad,
S.Y. Shin, Y.W. Koo (eds.): Proceedings of the 2007 ACM Symposium on
Applied Computing (SAC 2007), Seoul, Korea, March 11-15, 2007, ACM,
New York, NY, ISBN 1-59593-480-4 (2007) 5 Seiten.
- Kosheleva, O., Mayer, G., Kreinovich, V.: Towards a General
Description of Interval Multiplications: Algebraic Analysis and its
Relation to t-Norms.
In: Reformat, M., Berthold, M. R. (eds.):
Proceedings of the 2007 Annual Meeting of the North American Fuzzy
Information Processing Society (NAFIPS 2007), 24 June - 27 June,
2007, San Diego, California, USA, IEEE Press, Piscataway, NJ, ISBN
1-4244-1213-7, 543-548 (2007).
- Alefeld, G., Mayer, G.: New Criteria for the Feasibility of the
Cholesky Method for Interval Data.
SIAM J. Matrix Anal. Appl. 30 (4) 1392-1405 (2008).
- Mayer, G.: Direct Methods for Linear Systems with Inexact Input
Data.
JJIAM 26 (2-3), 279-296 (2009).
- Mayer, G.: An Oettli-Prager-like Theorem for the Symmetric Solution Set and for Realted Solution Sets.
SIAM J. Matrix Anal. Appl. 33 (3), 979-999 (2012).
- Mayer, G.: On an Expression for the Midpoint and the Radius of the Product of Two Intervals.
Reliable Computing 16, 210-224 (2012).
- Mayer, G.: Survey on Properties and Algorithms for the Symmetric Solution Set.
Preprint 12/2, Preprints aus dem Institut für Mathematik, Universität Rostock, Rostock, 2012, 58 Seiten
- Mayer, G.: Three Short Descriptions of the Symmetric and of the Skew-Symmetric Solution Set.
Linear Algebra Appl. 475, 73-79 (2015).
- Mayer, G.: Interval Analysis and Automatic Result Verification.
Studies in Mathematics, Band 65, De Gruyter, Berlin, Boston, 2017, ISBN 978-3-11-050063-9, Buch, 516 Seiten.