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Author ID: alefeld.gotz-e Recent zbMATH articles by "Alefeld, Götz E."
Published as: Alefeld, G.; Alefeld, Götz; Alefeld, G. E.; Alefeld, Goetz; Alefeld, Götz E.; Alefeld, Gotz
External Links: MGP · Wikidata · GND · IdRef
Documents Indexed: 133 Publications since 1968, including 3 Books
10 Contributions as Editor
Biographic References: 1 Publication
Co-Authors: 44 Co-Authors with 91 Joint Publications
1,404 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

103 Publications have been cited 1,451 times in 1,117 Documents Cited by Year
Introduction to interval computations. Transl. from the German by Jon Rokne. Zbl 0552.65041
Alefeld, Götz; Herzberger, Jürgen
632
1983
Interval analysis: Theory and applications. Zbl 0995.65056
Alefeld, Götz; Mayer, Günter
107
2000
Einführung in die Intervallrechnung. Zbl 0333.65002
Alefeld, Götz; Herzberger, Jürgen
70
1974
On the convergence speed of some algorithms for the simultaneous approximation of polynomial roots. Zbl 0282.65038
Alefeld, G.; Herzberger, J.
49
1974
On the convergence of Halley’s method. Zbl 0486.65035
Alefeld, G.
35
1981
Inclusion methods for systems of nonlinear equations – the interval Newton method and modifications. Zbl 0822.65029
Alefeld, G.
29
1994
On square roots of M-matrices. Zbl 0483.15009
Alefeld, G.; Schneider, N.
29
1982
Some efficient methods for enclosing simple zeros of nonlinear equations. Zbl 0756.65070
Alefeld, Götz E.; Potra, Florian A.
25
1992
Zur Konvergenz des symmetrischen Relaxationsverfahrens. Zbl 0319.65030
Alefeld, G.; Varga, R. S.
19
1976
The Cholesky method for interval data. Zbl 0796.65032
Alefeld, G.; Mayer, G.
16
1993
A quadratically convergent Krawczyk-like algorithm. Zbl 0505.65012
Alefeld, G.; Platzoeder, L.
16
1983
On enclosing simple roots of nonlinear equations. Zbl 0798.65062
Alefeld, G.; Potra, F. A.; Shi, Yixun
15
1993
On the convergence of some interval-arithmetic modifications of Newton’s method. Zbl 0536.65026
Alefeld, G.
15
1984
Algorithm 748: Enclosing zeros of continuous functions. Zbl 0888.65059
Alefeld, G. E.; Potra, F. A.; Shi, Y.
13
1995
Über die Durchführbarkeit des Gaußschen Algorithmus bei Gleichungen mit Intervallen als Koeffizienten. Zbl 0361.65017
Alefeld, G.
13
1977
On the symmetric and unsymmetric solution set of interval systems. Zbl 0834.65012
Alefeld, Götz; Mayer, Günter
12
1995
On the solution sets of particular classes of linear interval systems. Zbl 1019.65023
Alefeld, Götz; Kreinovich, Vladik; Mayer, Günter
12
2003
On the shape of the symmetric, persymmetric, and skew-symmetric solution set. Zbl 0873.15003
Alefeld, Götz; Kreinovich, Vladik; Mayer, Günter
12
1997
Efficient numerical validation of solutions of nonlinear systems. Zbl 0796.65068
Alefeld, G.; Gienger, A.; Potra, F.
12
1994
Regular splittings and monotone iteration functions. Zbl 0571.65043
Alefeld, Götz; Volkmann, Peter
12
1985
Iterative improvement of componentwise error bounds of invariant subspaces belonging to a double or nearly double eigenvalue. Zbl 0582.65026
Alefeld, G.; Spreuer, H.
11
1986
A regularized projection method for complementarity problems with non-Lipschitzian functions. Zbl 1171.90015
Alefeld, Goetz; Chen, Xiaojun
11
2008
Numerical validation of solutions of linear complementarity problems. Zbl 0933.65072
Alefeld, G. E.; Chen, X.; Potra, F. A.
11
1999
The shape of the solution set for systems of interval linear equations with dependent coefficients. Zbl 0907.15003
Alefeld, Götz; Kreinovich, Vladik; Mayer, Günter
10
1998
The basic properties of interval arithmetic, its software realizations and some applications. Zbl 0919.65034
Alefeld, G.; Claudio, D.
10
1998
On the existence theorems of Kantorovich, Moore and Miranda. Zbl 0995.65060
Alefeld, G. E.; Potra, F. A.; Shen, Z.
9
2001
Bounding the slope of polynomial operators and some applications. Zbl 0444.65027
Alefeld, G.
8
1981
Numerical validation of solutions of complementarity problems: the nonlinear case. Zbl 1040.65046
Alefeld, G. E.; Chen, X.; Potra, F. A.
8
2002
Über reguläre Zerlegungen bei nichtlinearen Abbildungen. Zbl 0258.65057
Alefeld, G.
8
1972
On the existence theorems of Kantorovich, Miranda and Borsuk. Zbl 1080.47042
Alefeld, Götz; Frommer, Andreas; Heindl, Gerhard; Mayer, Jan
8
2004
Über das Newton-Verfahren bei nichtlinearen Gleichungssystemen. Zbl 0283.65025
Alefeld, G.; Herzberger, J.
7
1970
Iterative methods for linear complementarity problems with interval data. Zbl 1029.90072
Alefeld, G.; Schäfer, U.
7
2003
A new class of interval methods with higher order of convergence. Zbl 0675.65041
Alefeld, G.; Potra, F.
7
1989
Intervallanalytische Methoden bei nichtlinearen Gleichungen. Zbl 0405.65022
Alefeld, Götz
7
1979
Über Simultanverfahren zur Bestimmung reeller Polynomwurzeln. Zbl 0293.65030
Alefeld, G.; Herzberger, J.
7
1974
Enclosing solutions of linear complementarity problems for H-matrices. Zbl 1074.65066
Alefeld, Götz; Wang, Zhengyu; Shen, Zuhe
7
2004
Enclosing solutions of singular interval systems iteratively. Zbl 1079.65027
Alefeld, Götz; Mayer, Günter
6
2005
On symmetric solution sets. Zbl 1038.65020
Alefeld, G.; Kreinovich, V.; Mayer, G.
6
2003
Zur Konvergenz des SSOR-Verfahrens für nichtlineare Gleichungssysteme. (Convergence of the SSOR method for nonlinear systems of simultaneous equations). Zbl 0631.65049
Alefeld, Götz; Volkmann, Peter
6
1986
On the convergence of the symmetric SOR method for matrices with red- black ordering. Zbl 0485.65024
Alefeld, G.
6
1982
On two higher order enclosing methods of J. W. Schmidt. Zbl 0657.65074
Alefeld, G.; Potra, F. A.
6
1988
Matrizeninvertierung mit Fehlererfassung. Zbl 0199.49702
Alefeld, G.; Herzberger, J.
5
1970
Über die aus monoton zerlegbaren Operatoren gebildeten Iterationsverfahren. Zbl 0211.46603
Alefeld, G.
5
1970
Nullstelleneinschließung mit dem Newton-Verfahren ohne Invertierung von Intervallmatrizen. Zbl 0238.65024
Alefeld, G.; Herzberger, J.
5
1972
New criteria for the feasibility of the Cholesky method with interval data. Zbl 1176.65023
Alefeld, G.; Mayer, G.
5
2008
Das symmetrische Einzelschrittverfahren bei linearen Gleichungen mit Intervallen als Koeffizienten. Zbl 0399.65019
Alefeld, G.
5
1977
Zur Konvergenz des Verfahrens der tangierenden Hyperbeln und des Tschebyscheff-Verfahrens bei konvexen Abbildungen. Zbl 0305.65025
Alefeld, G.
5
1973
On higher order centered forms. Zbl 0564.65031
Alefeld, G.; Lohner, R.
4
1985
Algorithm 748; enclosing zeros of continuous functions. Zbl 0872.65041
Alefeld, G. E.; Potra, F. A.; Shi, Yixun
4
1995
The shape of the symmetric solution set. Zbl 0841.15002
Alefeld, Götz; Kreinovich, Vladik; Mayer, Günter
4
1996
Monotone Regula-Falsi-ähnliche Verfahren bei nichtkonvexen Operatorgleichungen. Zbl 0425.65034
Alefeld, Götz
4
1980
On the evaluation of rational functions in interval arithmetic. Zbl 0463.65029
Alefeld, G.; Rokne, J. G.
4
1981
Über Eigenschaften und Anwendungsmöglichkeiten einer komplexen Intervallarithmetik. Zbl 0199.49701
Alefeld, G.
4
1970
Verfahren höherer Ordnung zur iterativen Einschließung der inversen Matrix. Zbl 0208.40101
Alefeld, Götz; Herzberger, Jürgen
4
1970
ALGOL-60 Algorithmen zur Auflösung linearer Gleichungssysteme mit Fehlererfassung. Zbl 0212.17002
Alefeld, G.; Herzberger, J.
4
1970
Validation numerics: theory and applications. Dedicated to Ulrich Kulisch on the occasion of his 60th birthday. Zbl 0784.00013
3
1993
Praktische Anwendung von Abschätzungsformeln bei Iterationsverfahren. Zbl 0187.09903
Alefeld, G.; Apostolatos, N.
3
1968
Verified numerical computation for nonlinear equations. Zbl 1186.65056
Alefeld, Goetz
3
2009
Berechenbare Fehlerschranken für ein Eigenpaar unter Einschluß von Rundungsfehlern bei Verwendung des genauen Skalarprodukts. (Computable error bounds for an eigenpair including roundoff-errors under application of the precise scalar product). Zbl 0622.65028
Alefeld, G.
3
1987
Error estimation for nonlinear complementarity problems via linear systems with interval data. Zbl 1154.90016
Alefeld, Götz; Wang, Zhengyu
3
2008
Error bounds for complementarity problems with tridiagonal nonlinear functions. Zbl 1183.65062
Alefeld, G.; Wang, Z.
3
2008
Quadratisch konvergente Einschließung von Lösungen nichtkonvexer Gleichungssysteme. Zbl 0294.65034
Alefeld, G.
3
1974
Verification algorithms for generalized singular values. Zbl 0939.65065
Alefeld, Götz; Hoffmann, Rolf; Mayer, Günter
3
1999
Stets konvergente Verfahren höherer Ordnung zur Berechnung von reellen Nullstellen. Zbl 0278.65045
Alefeld, G.
2
1974
Modifications of the interval-Newton-method with improved asymptotic efficiency. Zbl 0915.65040
Alefeld, G. E.; Potra, F. A.; Völker, W.
2
1998
Über die Verbesserung von Schranken für die Eigenwerte symmetrischer Tridiagonalmatrizen. Zbl 0267.65025
Alefeld, G.; Herzberger, J.
2
1974
Über die asymptotische Konvergenzgeschwindigkeit des allgemeinen Relaxationsverfahrens bei nichtnegativen Matrizen. Zbl 0181.17203
Alefeld, G.
2
1968
Anwendungen des Fixpunktsatzes für pseudometrische Räume in der Intervallrechnung. (Application of the fixed point theorem for pseudo- metric spaces in the interval arithmetic). Zbl 0222.65041
Alefeld, G.
2
1971
A device for the acceleration of convergence of a monotonously enclosing iteration method. Zbl 0522.65032
Cornelius, H.; Alefeld, G.
2
1982
A computer aided existence and uniqueness proof for an inverse matrix eigenvalue problem. Zbl 0834.65027
Alefeld, Götz; Mayer, Günter
2
1994
Eine Modifikation des Newtonverfahrens zur Bestimmung der reellen Nullstellen einer reellen Funktion. Zbl 0198.20903
Alefeld, G.
2
1970
Zur Invertierung linearer und beschränkter Operatoren. Zbl 0204.48003
Alefeld, G.; Herzberger, J.
2
1971
Über die Berechnung der inversen Matrix mit Hilfe der Intervallrechnung. Zbl 0208.40003
Alefeld, G.; Herzberger, J.
2
1970
Über die Verbesserung von Schranken für die Lösung bei linearen Gleichungssystemen. Zbl 0213.16304
Alefeld, G.; Herzberger, J.
2
1971
Über konvergente Zerlegungen von Matrizen. Zbl 0248.65021
Alefeld, G.
2
1973
Über die Existenz einer eindeutigen Lösung bei einer Klasse nichtlinearer Gleichungssysteme und deren Berechnung mit Iterationsverfahren. Zbl 0248.65035
Alefeld, Götz
2
1972
Enclosure methods. Zbl 0725.65050
Alefeld, G.
2
1990
Componentwise inclusion and exclusion sets for solutions of quadratic equations in finite dimensional spaces. Zbl 0597.65050
Alefeld, G.
2
1986
Zur iterativen Einschließung von positiven Inversen. Zbl 0403.65016
Alefeld, G.
2
1977
Über das Divergenzverhalten des Intervall-Newton-Verfahrens. (On the divergence behaviour of the interval-Newton-method). Zbl 0753.65044
Alefeld, G.
1
1991
On multisplitting methods for band matrices. Zbl 0878.65024
Alefeld, Götz; Lenhardt, Ingrid; Mayer, Günter
1
1997
On the convergence of the higher order versions of D. J. Evans’ implicit matrix inversion process. Zbl 0563.65012
Alefeld, G.
1
1984
Symmetric linear systems with perturbed input data. Zbl 0900.65132
Alefeld, G.; Kreinovich, V.; Mayer, G.
1
1996
Nonlinear structural finite element analysis using the preconditioned Lanczos method on serial and parallel computers. Zbl 0886.65051
Rottner, Th.; Lenhardt, I.; Alefeld, G.; Schweizerhof, K.
1
1997
Verallgemeinerung des Schulzschen Iterationsverfahrens. (Generalization of the iteration method by Schulz). Zbl 0222.65052
Alefeld, G.
1
1971
Über neuere Gesichtspunkte beim numerischen Rechnen. Zbl 0243.65019
Alefeld, G.; Herzberger, J.; Mayer, O.
1
1971
Scientific computing and validated numerics. Proceedings of the international symposium on scientific computing, computer arithmetic and validated numerics SCAN-95, Wuppertal, Germany, September 26-29, 1995. Zbl 0836.00039
1
1996
Effective improvements of the interval-Newton-method. Zbl 0848.65039
Alefeld, Götz E.; Potra, Florian A.; Völker, Wolfgang
1
1996
Fundamentals of numerical computation (computer-oriented numerical analysis). In cooperation with R. Albrecht, U. Kulisch, and F. Stummel. Zbl 0423.00017
1
1980
Bemerkungen zur Einschließung der Lösung eines linearen Gleichungssystems. Zbl 0198.20802
Alefeld, G.
1
1970
Numerical validation for an inverse matrix eigenvalue problem. Zbl 0813.65076
Alefeld, G.; Gienger, A.; Mayer, G.
1
1994
On the approximation of the range of values by interval expressions. Zbl 0722.65024
Alefeld, G.
1
1990
Berechenbare Fehlerschranken für ein Eigenpaar beim verallgemeinerten Eigenwertproblem. (Computable error bounds for an eigenpair of a generalized eigenvalue problem). Zbl 0647.65024
Alefeld, G.
1
1988
Über die Divergenzgeschwindigkeit des Intervall-Newton-Verfahrens. (On the speed of divergence of the interval-Newton method). Zbl 0727.65041
Alefeld, Götz
1
1990
Konvergenzbeschleunigende Maßnahmen bei einem Verfahren zur Einschließung von positiven Inversen. Zbl 0464.65030
Alefeld, Götz
1
1981
Zur numerischen Auflösung der Matrizengleichung \(AX^ 2-\)I=0. Zbl 0462.65022
Alefeld, Götz
1
1981
On improving approximate triangular factorizations iteratively. Zbl 0527.65017
Alefeld, Goetz; Rokne, Jon G.
1
1984
The centered form and the mean value form - a necessary condition that they yield the range. Zbl 0546.65025
Alefeld, G.
1
1984
Errorbounds for quadratic systems of nonlinear equations using the precise scalar product. Zbl 0658.65049
Alefeld, G.
1
1988
Symbolic algebraic methods and verification methods. Zbl 0963.00018
1
2001
Verified numerical computation for nonlinear equations. Zbl 1186.65056
Alefeld, Goetz
3
2009
A regularized projection method for complementarity problems with non-Lipschitzian functions. Zbl 1171.90015
Alefeld, Goetz; Chen, Xiaojun
11
2008
New criteria for the feasibility of the Cholesky method with interval data. Zbl 1176.65023
Alefeld, G.; Mayer, G.
5
2008
Error estimation for nonlinear complementarity problems via linear systems with interval data. Zbl 1154.90016
Alefeld, Götz; Wang, Zhengyu
3
2008
Error bounds for complementarity problems with tridiagonal nonlinear functions. Zbl 1183.65062
Alefeld, G.; Wang, Z.
3
2008
Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004). Selected papers based on the presentations at the 11th GAMM-IMACS international symposium, Fukuoka, Japan, October 4–8, 2004. Zbl 1127.68306
1
2007
Enclosing solutions of singular interval systems iteratively. Zbl 1079.65027
Alefeld, Götz; Mayer, Günter
6
2005
On the existence theorems of Kantorovich, Miranda and Borsuk. Zbl 1080.47042
Alefeld, Götz; Frommer, Andreas; Heindl, Gerhard; Mayer, Jan
8
2004
Enclosing solutions of linear complementarity problems for H-matrices. Zbl 1074.65066
Alefeld, Götz; Wang, Zhengyu; Shen, Zuhe
7
2004
On the solution sets of particular classes of linear interval systems. Zbl 1019.65023
Alefeld, Götz; Kreinovich, Vladik; Mayer, Günter
12
2003
Iterative methods for linear complementarity problems with interval data. Zbl 1029.90072
Alefeld, G.; Schäfer, U.
7
2003
On symmetric solution sets. Zbl 1038.65020
Alefeld, G.; Kreinovich, V.; Mayer, G.
6
2003
On the optimal solution of interval linear complementarity problems. Zbl 1354.90146
Alefeld, Götz; Schäfer, Uwe
1
2003
Numerical validation of solutions of complementarity problems: the nonlinear case. Zbl 1040.65046
Alefeld, G. E.; Chen, X.; Potra, F. A.
8
2002
On the existence theorems of Kantorovich, Moore and Miranda. Zbl 0995.65060
Alefeld, G. E.; Potra, F. A.; Shen, Z.
9
2001
Symbolic algebraic methods and verification methods. Zbl 0963.00018
1
2001
Interval analysis: Theory and applications. Zbl 0995.65056
Alefeld, Götz; Mayer, Günter
107
2000
Numerical validation of solutions of linear complementarity problems. Zbl 0933.65072
Alefeld, G. E.; Chen, X.; Potra, F. A.
11
1999
Verification algorithms for generalized singular values. Zbl 0939.65065
Alefeld, Götz; Hoffmann, Rolf; Mayer, Günter
3
1999
The shape of the solution set for systems of interval linear equations with dependent coefficients. Zbl 0907.15003
Alefeld, Götz; Kreinovich, Vladik; Mayer, Günter
10
1998
The basic properties of interval arithmetic, its software realizations and some applications. Zbl 0919.65034
Alefeld, G.; Claudio, D.
10
1998
Modifications of the interval-Newton-method with improved asymptotic efficiency. Zbl 0915.65040
Alefeld, G. E.; Potra, F. A.; Völker, W.
2
1998
On the shape of the symmetric, persymmetric, and skew-symmetric solution set. Zbl 0873.15003
Alefeld, Götz; Kreinovich, Vladik; Mayer, Günter
12
1997
On multisplitting methods for band matrices. Zbl 0878.65024
Alefeld, Götz; Lenhardt, Ingrid; Mayer, Günter
1
1997
Nonlinear structural finite element analysis using the preconditioned Lanczos method on serial and parallel computers. Zbl 0886.65051
Rottner, Th.; Lenhardt, I.; Alefeld, G.; Schweizerhof, K.
1
1997
The shape of the symmetric solution set. Zbl 0841.15002
Alefeld, Götz; Kreinovich, Vladik; Mayer, Günter
4
1996
Symmetric linear systems with perturbed input data. Zbl 0900.65132
Alefeld, G.; Kreinovich, V.; Mayer, G.
1
1996
Scientific computing and validated numerics. Proceedings of the international symposium on scientific computing, computer arithmetic and validated numerics SCAN-95, Wuppertal, Germany, September 26-29, 1995. Zbl 0836.00039
1
1996
Effective improvements of the interval-Newton-method. Zbl 0848.65039
Alefeld, Götz E.; Potra, Florian A.; Völker, Wolfgang
1
1996
Algorithm 748: Enclosing zeros of continuous functions. Zbl 0888.65059
Alefeld, G. E.; Potra, F. A.; Shi, Y.
13
1995
On the symmetric and unsymmetric solution set of interval systems. Zbl 0834.65012
Alefeld, Götz; Mayer, Günter
12
1995
Algorithm 748; enclosing zeros of continuous functions. Zbl 0872.65041
Alefeld, G. E.; Potra, F. A.; Shi, Yixun
4
1995
Inclusion methods for systems of nonlinear equations – the interval Newton method and modifications. Zbl 0822.65029
Alefeld, G.
29
1994
Efficient numerical validation of solutions of nonlinear systems. Zbl 0796.65068
Alefeld, G.; Gienger, A.; Potra, F.
12
1994
A computer aided existence and uniqueness proof for an inverse matrix eigenvalue problem. Zbl 0834.65027
Alefeld, Götz; Mayer, Günter
2
1994
Numerical validation for an inverse matrix eigenvalue problem. Zbl 0813.65076
Alefeld, G.; Gienger, A.; Mayer, G.
1
1994
The Cholesky method for interval data. Zbl 0796.65032
Alefeld, G.; Mayer, G.
16
1993
On enclosing simple roots of nonlinear equations. Zbl 0798.65062
Alefeld, G.; Potra, F. A.; Shi, Yixun
15
1993
Validation numerics: theory and applications. Dedicated to Ulrich Kulisch on the occasion of his 60th birthday. Zbl 0784.00013
3
1993
Some efficient methods for enclosing simple zeros of nonlinear equations. Zbl 0756.65070
Alefeld, Götz E.; Potra, Florian A.
25
1992
Über das Divergenzverhalten des Intervall-Newton-Verfahrens. (On the divergence behaviour of the interval-Newton-method). Zbl 0753.65044
Alefeld, G.
1
1991
Enclosure methods. Zbl 0725.65050
Alefeld, G.
2
1990
On the approximation of the range of values by interval expressions. Zbl 0722.65024
Alefeld, G.
1
1990
Über die Divergenzgeschwindigkeit des Intervall-Newton-Verfahrens. (On the speed of divergence of the interval-Newton method). Zbl 0727.65041
Alefeld, Götz
1
1990
A new class of interval methods with higher order of convergence. Zbl 0675.65041
Alefeld, G.; Potra, F.
7
1989
On two higher order enclosing methods of J. W. Schmidt. Zbl 0657.65074
Alefeld, G.; Potra, F. A.
6
1988
Berechenbare Fehlerschranken für ein Eigenpaar beim verallgemeinerten Eigenwertproblem. (Computable error bounds for an eigenpair of a generalized eigenvalue problem). Zbl 0647.65024
Alefeld, G.
1
1988
Errorbounds for quadratic systems of nonlinear equations using the precise scalar product. Zbl 0658.65049
Alefeld, G.
1
1988
Berechenbare Fehlerschranken für ein Eigenpaar unter Einschluß von Rundungsfehlern bei Verwendung des genauen Skalarprodukts. (Computable error bounds for an eigenpair including roundoff-errors under application of the precise scalar product). Zbl 0622.65028
Alefeld, G.
3
1987
Iterative improvement of componentwise error bounds of invariant subspaces belonging to a double or nearly double eigenvalue. Zbl 0582.65026
Alefeld, G.; Spreuer, H.
11
1986
Zur Konvergenz des SSOR-Verfahrens für nichtlineare Gleichungssysteme. (Convergence of the SSOR method for nonlinear systems of simultaneous equations). Zbl 0631.65049
Alefeld, Götz; Volkmann, Peter
6
1986
Componentwise inclusion and exclusion sets for solutions of quadratic equations in finite dimensional spaces. Zbl 0597.65050
Alefeld, G.
2
1986
Regular splittings and monotone iteration functions. Zbl 0571.65043
Alefeld, Götz; Volkmann, Peter
12
1985
On higher order centered forms. Zbl 0564.65031
Alefeld, G.; Lohner, R.
4
1985
On the convergence of some interval-arithmetic modifications of Newton’s method. Zbl 0536.65026
Alefeld, G.
15
1984
On the convergence of the higher order versions of D. J. Evans’ implicit matrix inversion process. Zbl 0563.65012
Alefeld, G.
1
1984
On improving approximate triangular factorizations iteratively. Zbl 0527.65017
Alefeld, Goetz; Rokne, Jon G.
1
1984
The centered form and the mean value form - a necessary condition that they yield the range. Zbl 0546.65025
Alefeld, G.
1
1984
Introduction to interval computations. Transl. from the German by Jon Rokne. Zbl 0552.65041
Alefeld, Götz; Herzberger, Jürgen
632
1983
A quadratically convergent Krawczyk-like algorithm. Zbl 0505.65012
Alefeld, G.; Platzoeder, L.
16
1983
On square roots of M-matrices. Zbl 0483.15009
Alefeld, G.; Schneider, N.
29
1982
On the convergence of the symmetric SOR method for matrices with red- black ordering. Zbl 0485.65024
Alefeld, G.
6
1982
A device for the acceleration of convergence of a monotonously enclosing iteration method. Zbl 0522.65032
Cornelius, H.; Alefeld, G.
2
1982
On the convergence of Halley’s method. Zbl 0486.65035
Alefeld, G.
35
1981
Bounding the slope of polynomial operators and some applications. Zbl 0444.65027
Alefeld, G.
8
1981
On the evaluation of rational functions in interval arithmetic. Zbl 0463.65029
Alefeld, G.; Rokne, J. G.
4
1981
Konvergenzbeschleunigende Maßnahmen bei einem Verfahren zur Einschließung von positiven Inversen. Zbl 0464.65030
Alefeld, Götz
1
1981
Zur numerischen Auflösung der Matrizengleichung \(AX^ 2-\)I=0. Zbl 0462.65022
Alefeld, Götz
1
1981
Monotone Regula-Falsi-ähnliche Verfahren bei nichtkonvexen Operatorgleichungen. Zbl 0425.65034
Alefeld, Götz
4
1980
Fundamentals of numerical computation (computer-oriented numerical analysis). In cooperation with R. Albrecht, U. Kulisch, and F. Stummel. Zbl 0423.00017
1
1980
Intervallanalytische Methoden bei nichtlinearen Gleichungen. Zbl 0405.65022
Alefeld, Götz
7
1979
Über die Durchführbarkeit des Gaußschen Algorithmus bei Gleichungen mit Intervallen als Koeffizienten. Zbl 0361.65017
Alefeld, G.
13
1977
Das symmetrische Einzelschrittverfahren bei linearen Gleichungen mit Intervallen als Koeffizienten. Zbl 0399.65019
Alefeld, G.
5
1977
Zur iterativen Einschließung von positiven Inversen. Zbl 0403.65016
Alefeld, G.
2
1977
An exclusion theorem for the solutions of operator equations. Zbl 0365.65039
Alefeld, Götz
1
1977
Zur Konvergenz des symmetrischen Relaxationsverfahrens. Zbl 0319.65030
Alefeld, G.; Varga, R. S.
19
1976
Einführung in die Intervallrechnung. Zbl 0333.65002
Alefeld, Götz; Herzberger, Jürgen
70
1974
On the convergence speed of some algorithms for the simultaneous approximation of polynomial roots. Zbl 0282.65038
Alefeld, G.; Herzberger, J.
49
1974
Über Simultanverfahren zur Bestimmung reeller Polynomwurzeln. Zbl 0293.65030
Alefeld, G.; Herzberger, J.
7
1974
Quadratisch konvergente Einschließung von Lösungen nichtkonvexer Gleichungssysteme. Zbl 0294.65034
Alefeld, G.
3
1974
Stets konvergente Verfahren höherer Ordnung zur Berechnung von reellen Nullstellen. Zbl 0278.65045
Alefeld, G.
2
1974
Über die Verbesserung von Schranken für die Eigenwerte symmetrischer Tridiagonalmatrizen. Zbl 0267.65025
Alefeld, G.; Herzberger, J.
2
1974
Zur Konvergenz des Verfahrens der tangierenden Hyperbeln und des Tschebyscheff-Verfahrens bei konvexen Abbildungen. Zbl 0305.65025
Alefeld, G.
5
1973
Über konvergente Zerlegungen von Matrizen. Zbl 0248.65021
Alefeld, G.
2
1973
Über reguläre Zerlegungen bei nichtlinearen Abbildungen. Zbl 0258.65057
Alefeld, G.
8
1972
Nullstelleneinschließung mit dem Newton-Verfahren ohne Invertierung von Intervallmatrizen. Zbl 0238.65024
Alefeld, G.; Herzberger, J.
5
1972
Über die Existenz einer eindeutigen Lösung bei einer Klasse nichtlinearer Gleichungssysteme und deren Berechnung mit Iterationsverfahren. Zbl 0248.65035
Alefeld, Götz
2
1972
Anwendungen des Fixpunktsatzes für pseudometrische Räume in der Intervallrechnung. (Application of the fixed point theorem for pseudo- metric spaces in the interval arithmetic). Zbl 0222.65041
Alefeld, G.
2
1971
Zur Invertierung linearer und beschränkter Operatoren. Zbl 0204.48003
Alefeld, G.; Herzberger, J.
2
1971
Über die Verbesserung von Schranken für die Lösung bei linearen Gleichungssystemen. Zbl 0213.16304
Alefeld, G.; Herzberger, J.
2
1971
Verallgemeinerung des Schulzschen Iterationsverfahrens. (Generalization of the iteration method by Schulz). Zbl 0222.65052
Alefeld, G.
1
1971
Über neuere Gesichtspunkte beim numerischen Rechnen. Zbl 0243.65019
Alefeld, G.; Herzberger, J.; Mayer, O.
1
1971
Über das Newton-Verfahren bei nichtlinearen Gleichungssystemen. Zbl 0283.65025
Alefeld, G.; Herzberger, J.
7
1970
Matrizeninvertierung mit Fehlererfassung. Zbl 0199.49702
Alefeld, G.; Herzberger, J.
5
1970
Über die aus monoton zerlegbaren Operatoren gebildeten Iterationsverfahren. Zbl 0211.46603
Alefeld, G.
5
1970
Über Eigenschaften und Anwendungsmöglichkeiten einer komplexen Intervallarithmetik. Zbl 0199.49701
Alefeld, G.
4
1970
Verfahren höherer Ordnung zur iterativen Einschließung der inversen Matrix. Zbl 0208.40101
Alefeld, Götz; Herzberger, Jürgen
4
1970
ALGOL-60 Algorithmen zur Auflösung linearer Gleichungssysteme mit Fehlererfassung. Zbl 0212.17002
Alefeld, G.; Herzberger, J.
4
1970
Eine Modifikation des Newtonverfahrens zur Bestimmung der reellen Nullstellen einer reellen Funktion. Zbl 0198.20903
Alefeld, G.
2
1970
Über die Berechnung der inversen Matrix mit Hilfe der Intervallrechnung. Zbl 0208.40003
Alefeld, G.; Herzberger, J.
2
1970
...and 3 more Documents
all top 5

Cited by 1,190 Authors

60 Petković, Miodrag S.
36 Alefeld, Götz E.
31 Mayer, Günter
25 Hladík, Milan
19 Herzberger, Jürgen P.
19 Qiu, Zhiping
19 Rokne, Jon G.
19 Rump, Siegfried Michael
18 Frommer, Andreas
17 Wolfe, Michael A.
13 Petković, Ljiljana D.
12 Tucker, Warwick
11 Chen, Xiaojun
11 Milošević, Dušan M.
11 Neumaier, Arnold
11 Schwandt, Hartmut
10 Popova, Evgeniya D.
8 Kearfott, Baker
8 Nakao, Mitsuhiro T.
8 Stefanović, Lidija V.
8 Wang, Zhengyu
8 Yamamura, Kiyotaka
7 Allahdadi, Mehdi
7 Carstensen, Carsten
7 Csendes, Tibor
7 Hashemi, Behnam
7 Ishibuchi, Hisao
7 Otadi, Mahmood
7 Rančić, Lidija Z.
7 Sharyĭ, Sergeĭ Petrovich
7 Shen, Zuhe
7 Wu, Hsien-Chung
6 Arana-Jiménez, Manuel
6 Bai, Zhongzhi
6 Chakraverty, Snehashish
6 Herceg, Đorđe D.
6 Jansson, Christian
6 Lin, Qun
6 Mosleh, Maryam
6 Neumann, Michael
6 Potra, Florian-Alexandru
6 Rohn, Jiri
6 Schäfer, Uwe
6 Schmidt, Jochen Wilhelm
6 Vrahatis, Michael N.
6 Watanabe, Yoshitaka
6 Yamamoto, Tetsuro
5 Abbasbandy, Saeid
5 Capinski, Maciej J.
5 Černý, Michal
5 Chen, Chin-Yun
5 Elishakoff, Isaac
5 Ghanbari, Mojtaba
5 Hernández, Miguel Ángel
5 Johnson, Tomas
5 Kyurkchiev, Nikolaĭ Veselinov
5 Mitsos, Alexander
5 Neher, Markus
5 Ratz, Dietmar
5 Skalna, Iwona
5 Wilczak, Daniel
5 Yamamoto, Nobito
5 Zgliczyński, Piotr
4 Allahviranloo, Tofigh
4 Antczak, Tadeusz
4 Barton, Paul I.
4 Dehghan Takht Fooladi, Mehdi
4 Domes, Ferenc
4 Franek, Peter
4 Galias, Zbigniew
4 Goldsztejn, Alexandre
4 Gupta, Dharmendra Kumar
4 Hadjidimos, Apostolos
4 Hofer, Eberhard P.
4 Ilić, Snežana M.
4 Kou, Jisheng
4 Kreinovich, Vladik Yakovlevich
4 Lang, Bruno
4 Lodwick, Weldon Alexander
4 Lotfi, Taher
4 Milošević, Mimica R.
4 Miyajima, Shinya
4 Nickel, Karl L. E.
4 Ratschek, Helmut
4 Schichl, Hermann
4 Shirayanagi, Kiyoshi
4 Soleymani, Fazlollah
4 Szyld, Daniel B.
4 Tibken, Bernd
4 Wang, Haijun
4 Wang, Xiaofeng
4 Wang, Xiaojun
4 Wang, Xiuhua
4 Wu, Xinyuan
4 Xiang, Shuhuang
3 Adams, Ernst Wilhelm
3 Arndt, Hans-Robert
3 Babenko, Ekaterina A.
3 Bánhelyi, Balázs
3 Barrio, Roberto
...and 1,090 more Authors
all top 5

Cited in 239 Serials

138 Computing
89 Journal of Computational and Applied Mathematics
64 Applied Mathematics and Computation
56 Linear Algebra and its Applications
38 Reliable Computing
31 Journal of Global Optimization
30 Computers & Mathematics with Applications
22 Numerische Mathematik
21 BIT
21 Fuzzy Sets and Systems
20 Numerical Algorithms
19 Applied Mathematical Modelling
17 Japan Journal of Industrial and Applied Mathematics
15 International Journal of Computer Mathematics
12 Information Sciences
12 Applied Numerical Mathematics
11 Computer Methods in Applied Mechanics and Engineering
11 Journal of Mathematical Analysis and Applications
10 Journal of Optimization Theory and Applications
9 Mathematics and Computers in Simulation
9 Theoretical Computer Science
8 Mathematics of Computation
8 Numerical Functional Analysis and Optimization
8 Communications in Nonlinear Science and Numerical Simulation
7 Mathematical Programming. Series A. Series B
7 Soft Computing
6 Automatica
6 Calcolo
6 Mathematical and Computer Modelling
6 European Journal of Operational Research
6 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
6 Numerical Linear Algebra with Applications
6 Journal of Applied Mathematics
6 Acta Mechanica Sinica
5 Applied Mathematics and Mechanics. (English Edition)
5 International Journal of Approximate Reasoning
5 Annals of Operations Research
5 SIAM Journal on Applied Dynamical Systems
5 BIT. Nordisk Tidskrift for Informationsbehandling
5 Nonlinear Analysis. Theory, Methods & Applications
4 Artificial Intelligence
4 Linear and Multilinear Algebra
4 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)
4 Aplikace Matematiky
4 Optimization
4 Applications of Mathematics
4 International Journal of Robust and Nonlinear Control
4 Cybernetics and Systems Analysis
4 Nonlinear Dynamics
4 Journal of Industrial and Management Optimization
4 Optimization Letters
3 Journal of the Franklin Institute
3 Journal of Differential Equations
3 Topology and its Applications
3 Systems & Control Letters
3 SIAM Journal on Algebraic and Discrete Methods
3 Discrete & Computational Geometry
3 Computers & Operations Research
3 Applied Mathematics Letters
3 Computational Statistics
3 Computational Optimization and Applications
3 Journal of Computer and Systems Sciences International
3 International Applied Mechanics
3 Computational and Applied Mathematics
3 Mathematical Problems in Engineering
3 CEJOR. Central European Journal of Operations Research
3 International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
3 Differential Equations
3 Fuzzy Optimization and Decision Making
3 Advances in Difference Equations
3 Mathematics in Computer Science
3 International Journal of Systems Science. Principles and Applications of Systems and Integration
2 Mathematical Methods in the Applied Sciences
2 Periodica Mathematica Hungarica
2 ACM Transactions on Mathematical Software
2 Meccanica
2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
2 Opsearch
2 Physica D
2 Journal of Symbolic Computation
2 Journal of Complexity
2 Computational Mechanics
2 Asia-Pacific Journal of Operational Research
2 SIAM Journal on Matrix Analysis and Applications
2 Journal of Scientific Computing
2 YUJOR. Yugoslav Journal of Operations Research
2 Computational Statistics and Data Analysis
2 Computers and Mathematics with Applications. Part A
2 The Journal of Analysis
2 Applied Mathematics. Series B (English Edition)
2 Journal of Mathematical Sciences (New York)
2 Turkish Journal of Mathematics
2 Engineering Analysis with Boundary Elements
2 ELA. The Electronic Journal of Linear Algebra
2 Abstract and Applied Analysis
2 Optimization Methods & Software
2 Discrete Dynamics in Nature and Society
2 Regular and Chaotic Dynamics
2 International Journal of Applied Mathematics and Computer Science
2 Central European Journal of Mathematics
...and 139 more Serials
all top 5

Cited in 52 Fields

814 Numerical analysis (65-XX)
204 Operations research, mathematical programming (90-XX)
96 Linear and multilinear algebra; matrix theory (15-XX)
91 Computer science (68-XX)
84 Functions of a complex variable (30-XX)
56 Real functions (26-XX)
53 Ordinary differential equations (34-XX)
47 Systems theory; control (93-XX)
45 Field theory and polynomials (12-XX)
44 Mechanics of deformable solids (74-XX)
42 Operator theory (47-XX)
32 Dynamical systems and ergodic theory (37-XX)
29 Statistics (62-XX)
26 Partial differential equations (35-XX)
25 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
24 Mathematical logic and foundations (03-XX)
23 Calculus of variations and optimal control; optimization (49-XX)
20 Mechanics of particles and systems (70-XX)
19 Approximations and expansions (41-XX)
14 Probability theory and stochastic processes (60-XX)
13 Biology and other natural sciences (92-XX)
8 Fluid mechanics (76-XX)
8 Information and communication theory, circuits (94-XX)
7 Convex and discrete geometry (52-XX)
6 Integral equations (45-XX)
6 Algebraic topology (55-XX)
5 Special functions (33-XX)
5 Difference and functional equations (39-XX)
5 Functional analysis (46-XX)
4 Combinatorics (05-XX)
4 Order, lattices, ordered algebraic structures (06-XX)
4 Measure and integration (28-XX)
4 General topology (54-XX)
3 General algebraic systems (08-XX)
3 Number theory (11-XX)
3 Harmonic analysis on Euclidean spaces (42-XX)
3 Geophysics (86-XX)
2 Commutative algebra (13-XX)
2 Associative rings and algebras (16-XX)
2 Sequences, series, summability (40-XX)
2 Optics, electromagnetic theory (78-XX)
2 Quantum theory (81-XX)
1 General and overarching topics; collections (00-XX)
1 History and biography (01-XX)
1 Algebraic geometry (14-XX)
1 Nonassociative rings and algebras (17-XX)
1 Group theory and generalizations (20-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Geometry (51-XX)
1 Differential geometry (53-XX)
1 Classical thermodynamics, heat transfer (80-XX)
1 Statistical mechanics, structure of matter (82-XX)

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