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Author ID: frommer.andreas Recent zbMATH articles by "Frommer, Andreas"
Published as: Frommer, Andreas; Frommer, A.
Homepage: http://www-ai.math.uni-wuppertal.de/~frommer/
External Links: MGP · Wikidata · dblp · GND
Documents Indexed: 126 Publications since 1986, including 3 Books
7 Contributions as Editor
Reviewing Activity: 40 Reviews
Co-Authors: 99 Co-Authors with 110 Joint Publications
1,763 Co-Co-Authors
all top 5

Co-Authors

23 single-authored
18 Mayer, Günter
18 Szyld, Daniel B.
10 Lang, Bruno
8 Lippert, Thomas
7 Schweitzer, Marcel
5 Hashemi, Behnam
5 Schilling, Klaus-Jürgen
4 Monien, Burkhard
4 Müller, Peter Chr.
4 Nabben, Reinhard
4 Qiu, Zhiping
4 Schwandt, Hartmut
3 Alefeld, Götz E.
3 Brannick, James J.
3 Diekmann, Ralf
3 Kahl, Karsten
3 Krieg, Stefan
3 Lund, Kathryn
3 Medeke, Björn
3 Schimmel, Claudia
2 Arnold, Guido
2 Beelitz, Thomas
2 Bietenholz, Wolfgang
2 Birk, Sebastian
2 Bloch, Jacques C. R.
2 Bolten, Matthias
2 Chen, Xiaojun
2 Cundy, Nigel
2 Cvetković, Ljiljana
2 Eicker, N.
2 Foerster, Hildegard
2 Fritzsche, David
2 Glässner, Uwe
2 Güttel, Stefan
2 Leder, Björn
2 Pohl, Bert
2 Renaut, Rosemary Anne
2 Rottmann, Matthias
2 Schäfer, Katrin
2 Simoncini, Valeria
2 Spiteri, Pierre
2 van den Eshof, Jasper
2 Weinberg, Andre
2 Wettig, Tilo
2 Willems, Paul R.
2 Wyss, Christian
2 Zwaan, Ian N.
1 Alt, René
1 Benzi, Michele
1 Block, U.
1 Boriçi, Artan
1 Brandt, Achi E.
1 Breu, Tobias
1 Chow, Edmond G. W.
1 Ebadi, Ghodrat
1 El Baz, Didier
1 Elsässer, Robert
1 Elsner, Ludwig F.
1 Friedhoff, Stephanie
1 Großer, Benedikt
1 Heindl, Gerhard
1 Heming, Matthias
1 Heybrock, Simon
1 Hoxha, Fatmir
1 Hwang, Suk-Geun
1 Jacob, Birgit
1 Jacob, Brigit
1 Joó, Bálint
1 Kahl, Kartsen
1 Kearfott, Baker
1 Kennedy, Anthony D.
1 Khalil, Mostafa Nasr
1 Kolotilina, Lily Yu.
1 Krivsky, Stefanie
1 Kummert, Anton
1 Li, Yingbo
1 Livshits, Irene
1 Long, Bruno
1 Luther, Wolfram Jérôme
1 Maass, Peter
1 MacLachlan, Scott P.
1 Mayer, Jan
1 Pendleton, Brian
1 Preis, Robert
1 Ramirez-Hidalgo, Gustavo
1 Rashedi, Somaiyeh
1 Rittich, H.
1 Sablik, Thomas
1 Scheid, Harald
1 Schneider, Hans
1 Shank, Stephen D.
1 Šmigoc, Helena
1 Straub, W. D.
1 Strebel, Artur
1 Tapamo, H.
1 Van der Vorst, Henk Albertus
1 Vorberg, Lukas A.
1 Zhang, Fuzhen
1 Zikatanov, Ludmil T.

Publications by Year

Citations contained in zbMATH Open

105 Publications have been cited 1,124 times in 772 Documents Cited by Year
Convergence of relaxed parallel multisplitting methods. Zbl 0676.65022
Frommer, Andreas; Mayer, Günter
150
1989
\(H\)-splittings and two-stage iterative methods. Zbl 0764.65018
Frommer, Andreas; Szyld, Daniel B.
105
1992
Restarted GMRES for shifted linear systems. Zbl 0912.65023
Frommer, Andreas; Glässner, Uwe
43
1998
Efficient and stable Arnoldi restarts for matrix functions based on quadrature. Zbl 1309.65050
Frommer, Andreas; Güttel, Stefan; Schweitzer, Marcel
40
2014
On asynchronous iterations. Zbl 0967.65066
Frommer, Andreas; Szyld, Daniel B.
38
2000
Algebraic theory of multiplicative Schwarz methods. Zbl 0991.65037
Benzi, Michele; Frommer, Andreas; Nabben, Reinhard; Szyld, Daniel B.
36
2001
Weighted max norms, splittings, and overlapping additive Schwarz iterations. Zbl 0934.65035
Frommer, Andreas; Szyld, Daniel B.
36
1999
Asynchronous two-stage iterative methods. Zbl 0821.65010
Frommer, Andreas; Szyld, Daniel B.
29
1994
Fast cg-based methods for Tikhonov–Phillips regularization. Zbl 0943.65068
Frommer, Andreas; Maass, Peter
29
1999
BiCGStab(\(\ell\)) for families of shifted linear systems. Zbl 1239.65022
Frommer, Andreas
29
2003
An algebraic convergence theory for restricted additive Schwarz methods using weighted max norms. Zbl 1006.65031
Frommer, Andreas; Szyld, Daniel B.
28
2001
Numerical methods for the QCDd overlap operator. I: Sign-function and error bounds. Zbl 1008.81508
van den Eshof, J.; Frommer, A.; Lippert, Th.; Schilling, K.; van der Vorst, H. A.
27
2002
Matrix functions. Zbl 1153.65333
Frommer, Andreas; Simoncini, Valeria
24
2008
Numerical challenges in lattice quantum chromodynamics. Joint interdisciplinary workshop of John von Neumann Institute for Computing, Jülich, and Institute of Applied Computer Science, Wuppertal Univ., Germany, August 1999. Zbl 0957.00052
20
2000
Computational existence proofs for spherical \(t\)-designs. Zbl 1208.65032
Chen, Xiaojun; Frommer, Andreas; Lang, Bruno
20
2011
Block Krylov subspace methods for functions of matrices. Zbl 1372.65138
Frommer, Andreas; Lund, Kathryn; Szyld, Daniel B.
20
2017
Convergence of restarted Krylov subspace methods for Stieltjes functions of matrices. Zbl 1316.65040
Frommer, Andreas; Güttel, Stefan; Schweitzer, Marcel
18
2014
Stopping criteria for rational matrix functions of Hermitian and symmetric matrices. Zbl 1203.65079
Frommer, Andreas; Simoncini, Valeria
18
2008
Efficient schemes for nearest neighbor load balancing. Zbl 0942.90023
Diekmann, R.; Frommer, A.; Monien, B.
17
1999
Parallel nonlinear multisplitting methods. Zbl 0662.65042
Frommer, Andreas
16
1989
On the theory and practice of multisplitting methods in parallel computation. Zbl 0763.65019
Frommer, A.; Mayer, G.
15
1992
Verified computation of square roots of a matrix. Zbl 1194.65069
Frommer, Andreas; Hashemi, Behnam
14
2010
Parallel interval multisplittings. Zbl 0682.65016
Frommer, Andreas; Mayer, Günter
14
1989
Asynchronous weighted additive Schwarz methods. Zbl 0890.65027
Frommer, Andreas; Schwandt, Hartmut; Szyld, Daniel B.
13
1997
Conditions for strict inequality in comparisons of spectral radii of splittings of different matrices. Zbl 1018.65049
Elsner, Ludwig; Frommer, Andreas; Nabben, Reinhard; Schneider, Hans; Szyld, Daniel B.
13
2003
A unified representation and theory of algebraic additive Schwarz and multisplitting methods. Zbl 0892.65017
Frommer, Andreas; Schwandt, Hartmut
12
1997
A comparison result for multisplittings and waveform relaxation methods. Zbl 0831.65031
Frommer, Andreas; Pohl, Bert
11
1995
Generalized nonlinear diagonal dominance and applications to asynchronous iterative methods. Zbl 0746.65046
Frommer, Andreas
10
1991
An iterative method to compute the sign function of a non-Hermitian matrix and its application to the overlap Dirac operator at nonzero chemical potential. Zbl 1196.65085
Bloch, J.; Frommer, A.; Lang, B.; Wettig, T.
10
2007
A unified approach to method for the simultaneous computation of all zeros of generalized polynomials. Zbl 0636.65045
Frommer, Andreas
9
1988
Adaptive aggregation-based domain decomposition multigrid for the lattice Wilson-Dirac operator. Zbl 1302.81159
Frommer, A.; Kahl, K.; Krieg, S.; Leder, B.; Rottmann, M.
9
2014
A new criterion to guarantee the feasibility of the interval Gaussian algorithm. Zbl 0777.65012
Frommer, A.; Mayer, G.
8
1993
A comparison of the Moore and Miranda existence tests. Zbl 1069.47060
Frommer, A.; Lang, B.; Schnurr, M.
8
2004
The new nonprobabilistic criterion of failure for dynamical systems based on convex models. Zbl 1112.93038
Qiu, Z. P.; Mueller, P. C.; Frommer, A.
8
2004
Monotone convergence of the Lanczos approximations to matrix functions of Hermitian matrices. Zbl 1190.65063
Frommer, Andreas
8
2009
Verified error bounds for solutions of Sylvester matrix equations. Zbl 1236.65045
Frommer, Andreas; Hashemi, Behnam
8
2012
Computing enclosures for the inverse square root and the sign function of a matrix. Zbl 1293.65071
Frommer, Andreas; Hashemi, Behnam; Sablik, Thomas
8
2014
An approximate method for the standard interval eigenvalue problem of real non-symmetric interval matrices. Zbl 0991.65040
Qiu, Zhiping; Müller, Peter C.; Frommer, Andreas
7
2001
On the existence theorems of Kantorovich, Miranda and Borsuk. Zbl 1080.47042
Alefeld, Götz; Frommer, Andreas; Heindl, Gerhard; Mayer, Jan
7
2004
Existence tests for solutions of nonlinear equations using Borsuk’s theorem. Zbl 1095.47057
Frommer, Andreas; Lang, Bruno
7
2005
Adaptive reduction-based multigrid for nearly singular and highly disordered physical systems. Zbl 1205.65321
Brannick, J.; Frommer, A.; Kahl, K.; Maclachlan, S.; Zikatanov, L.
7
2010
Analysis of probing techniques for sparse approximation and trace estimation of decaying matrix functions. Zbl 07398755
Frommer, Andreas; Schimmel, Claudia; Schweitzer, Marcel
6
2021
Lösung linearer Gleichungssysteme auf Parallelrechnern. (Solution of systems of linear equations on parallel computers). Zbl 0706.65014
Frommer, Andreas
6
1990
Short-recurrence Krylov subspace methods for the overlap Dirac operator at nonzero chemical potential. Zbl 1219.81096
Bloch, Jacques C. R.; Breu, Tobias; Frommer, Andreas; Heybrock, Simon; Schäfer, Katrin; Wettig, Tilo
6
2010
Convergence of stationary iterative methods for Hermitian semidefinite linear systems and applications to Schwarz methods. Zbl 1165.65012
Frommer, Andreas; Nabben, Reinhard; Szyld, Daniel B.
6
2008
On asynchronous iterations in partially ordered spaces. Zbl 0724.65063
Frommer, Andreas
6
1991
Comparison of Brown’s and Newton’s method in the monotone case. Zbl 0628.65039
Frommer, Andreas
5
1988
A linear programming based analysis of the CP-rank of completely positive matrices. Zbl 1171.90471
Li, Yingbo; Kummert, Anton; Frommer, Andreas
5
2004
On the R-order of Newton-like methods for enclosing solutions of nonlinear equations. Zbl 0691.65031
Frommer, Andreas; Mayer, Günter
5
1990
Block colouring schemes for the SOR method on local memory parallel computers. Zbl 0699.65020
Block, U.; Frommer, A.; Mayer, G.
5
1990
2-norm error bounds and estimates for Lanczos approximations to linear systems and rational matrix functions. Zbl 1283.65020
Frommer, A.; Kahl, K.; Lippert, Th.; Rittich, H.
5
2013
Bounds for the decay of the entries in inverses and Cauchy-Stieltjes functions of certain sparse, normal matrices. Zbl 06945797
Frommer, Andreas; Schimmel, Claudia; Schweitzer, Marcel
5
2018
Non-Toeplitz decay bounds for inverses of Hermitian positive definite tridiagonal matrices. Zbl 1402.15020
Frommer, Andreas; Schimmel, Claudia; Schweitzer, Marcel
5
2018
Stability robustness bounds for linear state-space models with structured uncertainty based on ellipsoidal set-theoretic approach. Zbl 1066.93043
Qiu, Zhiping; Müller, Peter C.; Frommer, Andreas
4
2001
Proving conjectures by use of interval arithmetic. Zbl 0990.65048
Frommer, Andreas
4
2001
Numerical methods for the QCD overlap operator. II: Optimal Krylov subspace methods. Zbl 1077.81528
Arnold, Guido; Cundy, Nigel; van den Eshof, Jasper; Frommer, Andreas; Krieg, Stefan; Lippert, Thomas; Schäfer, Katrin
4
2005
Algebraic multigrid methods for Laplacians of graphs. Zbl 1217.65063
Bolten, Matthias; Friedhoff, Stephanie; Frommer, Andreas; Heming, Matthias; Kahl, Karsten
4
2011
Error bounds and estimates for Krylov subspace approximations of Stieltjes matrix functions. Zbl 1353.65038
Frommer, Andreas; Schweitzer, Marcel
4
2016
On short recurrence Krylov type methods for linear systems with many right-hand sides. Zbl 1382.65092
Rashedi, Somaiyeh; Ebadi, Ghodrat; Birk, Sebastian; Frommer, Andreas
4
2016
A deflated conjugate gradient method for multiple right hand sides and multiple shifts. Zbl 1305.65116
Birk, Sebastian; Frommer, Andreas
4
2014
Efficient schemes for nearest neighbor load balancing. Zbl 0930.68163
Diekmann, Ralf; Frommer, Andreas; Monien, Burkhard
3
1999
Optimal and alternating-direction load balancing schemes. Zbl 0947.68008
Elsässer, Robert; Frommer, Andreas; Monien, Burkhard; Preis, Robert
3
1999
Ellipsoidal set-theoretic approach for stability of linear state-space models with interval uncertainty. Zbl 0985.65077
Qiu, Zhiping; Müller, Peter C.; Frommer, Andreas
3
2001
Asynchronous parallel methods for enclosing solutions of nonlinear equations. Zbl 0837.65051
Frommer, Andreas; Schwandt, Hartmut
3
1995
Asynchronous iterations with flexible communication: contracting operators. Zbl 1069.65054
El Baz, Didier; Frommer, Andreas; Spiteri, Pierre
3
2005
Monotonie und Einschließung beim Brown-Verfahren. Zbl 0613.65051
Frommer, Andreas
3
1986
Monotonicity of Brown’s method. Zbl 0646.65043
Frommer, A.
3
1988
An algebraic convergence theory for restricted additive and multiplicative Schwarz methods. Zbl 1026.65022
Frommer, A.; Nabben, R.; Szyld, D. B.
3
2002
Block Krylov subspace methods for functions of matrices. II: Modified block FOM. Zbl 1441.65051
Frommer, Andreas; Lund, Kathryn; Szyld, Daniel B.
3
2020
Symbolic-numeric techniques for solving nonlinear systems. Zbl 1391.65143
Beelitz, Thomas; Frommer, Andreas; Lang, Bruno; Willems, Paul
2
2005
A unified approach to parallel space decomposition methods. Zbl 0936.65071
Frommer, Andreas; Renaut, Rosemary A.
2
1999
A feasibility result for interval Gaussian elimination relying on graph structure. Zbl 0984.65020
Frommer, Andreas
2
2001
QCD and numerical analysis III. Proceedings of the third international workshop on numerical analysis and lattice QCD, Edinburgh, UK, June 30 – July 4, 2003. Zbl 1066.81001
2
2005
Numerical software with result verification. International Dagstuhl seminar, Dagstuhl Castle, Germany, January 19–24, 2003. Revised papers. Zbl 1046.65001
2
2004
Monotonicity of Brown’s method. Zbl 0663.65047
Frommer, A.
2
1988
On preconditioners for the Borsuk existence test. Zbl 1354.65098
Frommer, Andreas; Lang, Bruno
2
2004
Multigrid preconditioning for the overlap operator in lattice QCD. Zbl 1333.81426
Brannick, James; Frommer, Andreas; Kahl, Karsten; Leder, Björn; Rottmann, Matthias; Strebel, Artur
2
2016
On necessary conditions for convergence of stationary iterative methods for Hermitian semidefinite linear systems. Zbl 1320.65049
Frommer, Andreas; Szyld, Daniel B.
2
2014
Proving the existence of zeros using the topological degree and interval arithmetic. Zbl 1129.65037
Frommer, A.; Hoxha, F.; Lang, B.
2
2007
Generalized diagonal dominance of nonlinear functions. II: Application to asynchronous iterative methods and examples. (Verallgemeinerte Diagonaldominanz bei nichtlinearen Funktionen. II: Anwendung auf asynchrone Iterationsverfahren und Beispiele.) Zbl 0786.65045
Frommer, A.
2
1992
The Radau-Lanczos method for matrix functions. Zbl 1371.65042
Frommer, Andreas; Lund, Kathryn; Schweitzer, Marcel; Szyld, Daniel B.
2
2017
Theoretische und praktische Ergebnisse zu Multisplitting-Verfahren auf Parallelrechnern. (Theoretical and practical results of multisplitting methods on parallel computers). Zbl 0714.65038
Frommer, A.; Mayer, G.
2
1990
Efficient methods for enclosing solutions of systems of nonlinear equations. Zbl 0721.65025
Frommer, A.; Mayer, G.
2
1990
Verified stability analysis using the Lyapunov matrix equation. Zbl 1288.65058
Frommer, Andreas; Hashemi, Behnam
2
2013
Safe bounds for the solutions of nonlinear problems using a parallel multisplitting method. Zbl 0685.65045
Frommer, A.; Mayer, G.
2
1989
Scalable parallel SSOR preconditioning for lattice computations in gauge theories. Zbl 0996.68823
Frommer, A.; Lippert, Th.; Schilling, K.
2
1997
A bootstrap algebraic multilevel method for Markov chains. Zbl 1269.65033
Bolten, Matthias; Brandt, Achi; Brannick, James; Frommer, Andreas; Kahl, Karsten; Livshits, Ira
2
2011
Computing enclosures for the matrix exponential. Zbl 1459.65056
Frommer, Andreas; Hashemi, Behnam
2
2020
Two-stage interval iterative methods. Zbl 0790.65020
Frommer, A.; Mayer, G.
1
1993
Comparison results for splittings based on overlapping blocks. Zbl 0819.65038
Frommer, Andreas; Pohl, Bert
1
1994
Extensions of certain graph-based algorithms for preconditioning. Zbl 1149.65033
Fritzsche, David; Frommer, Andreas; Szyld, Daniel B.
1
2007
Parallel space decomposition for minimization of nonlinear functionals. Zbl 0945.65064
Frommer, Andreas; Renaut, Rosemary A.
1
1999
Verified error bounds for linear systems through the Lanczos process. Zbl 1067.65041
Frommer, Andreas; Weinberg, Andre
1
1999
Asynchronous iterations for enclosing solutions of fixed point problems. Zbl 0838.65061
Frommer, Andreas
1
1992
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
Linear systems with \(\Omega\)-diagonally dominant matrices and related ones. Zbl 0774.65013
Frommer, A.; Mayer, G.
1
1993
Asynchronous iterations for enclosing solutions. Zbl 0900.65155
Frommer, A.
1
1996
Implementing Brown’s method for systems of nonlinear equations with dense banded Jacobian. Zbl 0662.65043
Frommer, A.
1
1989
Iterationsverfahren für lineare Gleichungssysteme auf Parallelrechnern. (Iterative methods for systems of linear equations on parallel computers). Zbl 0735.65013
Frommer, A.; Mayer, G.
1
1991
Numerical methods for the QCD overlap operator IV: Hybrid Monte Carlo. Zbl 1198.81013
Cundy, N.; Krieg, S.; Arnold, G.; Frommer, A.; Lippert, Th.; Schilling, K.
1
2009
Analysis of probing techniques for sparse approximation and trace estimation of decaying matrix functions. Zbl 07398755
Frommer, Andreas; Schimmel, Claudia; Schweitzer, Marcel
6
2021
Block Krylov subspace methods for functions of matrices. II: Modified block FOM. Zbl 1441.65051
Frommer, Andreas; Lund, Kathryn; Szyld, Daniel B.
3
2020
Computing enclosures for the matrix exponential. Zbl 1459.65056
Frommer, Andreas; Hashemi, Behnam
2
2020
Bounds for the decay of the entries in inverses and Cauchy-Stieltjes functions of certain sparse, normal matrices. Zbl 06945797
Frommer, Andreas; Schimmel, Claudia; Schweitzer, Marcel
5
2018
Non-Toeplitz decay bounds for inverses of Hermitian positive definite tridiagonal matrices. Zbl 1402.15020
Frommer, Andreas; Schimmel, Claudia; Schweitzer, Marcel
5
2018
Block Krylov subspace methods for functions of matrices. Zbl 1372.65138
Frommer, Andreas; Lund, Kathryn; Szyld, Daniel B.
20
2017
The Radau-Lanczos method for matrix functions. Zbl 1371.65042
Frommer, Andreas; Lund, Kathryn; Schweitzer, Marcel; Szyld, Daniel B.
2
2017
Error bounds and estimates for Krylov subspace approximations of Stieltjes matrix functions. Zbl 1353.65038
Frommer, Andreas; Schweitzer, Marcel
4
2016
On short recurrence Krylov type methods for linear systems with many right-hand sides. Zbl 1382.65092
Rashedi, Somaiyeh; Ebadi, Ghodrat; Birk, Sebastian; Frommer, Andreas
4
2016
Multigrid preconditioning for the overlap operator in lattice QCD. Zbl 1333.81426
Brannick, James; Frommer, Andreas; Kahl, Karsten; Leder, Björn; Rottmann, Matthias; Strebel, Artur
2
2016
Efficient and stable Arnoldi restarts for matrix functions based on quadrature. Zbl 1309.65050
Frommer, Andreas; Güttel, Stefan; Schweitzer, Marcel
40
2014
Convergence of restarted Krylov subspace methods for Stieltjes functions of matrices. Zbl 1316.65040
Frommer, Andreas; Güttel, Stefan; Schweitzer, Marcel
18
2014
Adaptive aggregation-based domain decomposition multigrid for the lattice Wilson-Dirac operator. Zbl 1302.81159
Frommer, A.; Kahl, K.; Krieg, S.; Leder, B.; Rottmann, M.
9
2014
Computing enclosures for the inverse square root and the sign function of a matrix. Zbl 1293.65071
Frommer, Andreas; Hashemi, Behnam; Sablik, Thomas
8
2014
A deflated conjugate gradient method for multiple right hand sides and multiple shifts. Zbl 1305.65116
Birk, Sebastian; Frommer, Andreas
4
2014
On necessary conditions for convergence of stationary iterative methods for Hermitian semidefinite linear systems. Zbl 1320.65049
Frommer, Andreas; Szyld, Daniel B.
2
2014
2-norm error bounds and estimates for Lanczos approximations to linear systems and rational matrix functions. Zbl 1283.65020
Frommer, A.; Kahl, K.; Lippert, Th.; Rittich, H.
5
2013
Verified stability analysis using the Lyapunov matrix equation. Zbl 1288.65058
Frommer, Andreas; Hashemi, Behnam
2
2013
Overlapping blocks by growing a partition with applications to preconditioning. Zbl 1268.65044
Fritzsche, David; Frommer, Andreas; Shank, Stephen D.; Szyld, Daniel B.
1
2013
Verified error bounds for solutions of Sylvester matrix equations. Zbl 1236.65045
Frommer, Andreas; Hashemi, Behnam
8
2012
Computational existence proofs for spherical \(t\)-designs. Zbl 1208.65032
Chen, Xiaojun; Frommer, Andreas; Lang, Bruno
20
2011
Algebraic multigrid methods for Laplacians of graphs. Zbl 1217.65063
Bolten, Matthias; Friedhoff, Stephanie; Frommer, Andreas; Heming, Matthias; Kahl, Karsten
4
2011
A bootstrap algebraic multilevel method for Markov chains. Zbl 1269.65033
Bolten, Matthias; Brandt, Achi; Brannick, James; Frommer, Andreas; Kahl, Karsten; Livshits, Ira
2
2011
Verified computation of square roots of a matrix. Zbl 1194.65069
Frommer, Andreas; Hashemi, Behnam
14
2010
Adaptive reduction-based multigrid for nearly singular and highly disordered physical systems. Zbl 1205.65321
Brannick, J.; Frommer, A.; Kahl, K.; Maclachlan, S.; Zikatanov, L.
7
2010
Short-recurrence Krylov subspace methods for the overlap Dirac operator at nonzero chemical potential. Zbl 1219.81096
Bloch, Jacques C. R.; Breu, Tobias; Frommer, Andreas; Heybrock, Simon; Schäfer, Katrin; Wettig, Tilo
6
2010
Monotone convergence of the Lanczos approximations to matrix functions of Hermitian matrices. Zbl 1190.65063
Frommer, Andreas
8
2009
Numerical methods for the QCD overlap operator IV: Hybrid Monte Carlo. Zbl 1198.81013
Cundy, N.; Krieg, S.; Arnold, G.; Frommer, A.; Lippert, Th.; Schilling, K.
1
2009
A framework for existence tests based on the topological degree and homotopy. Zbl 1163.65024
Beelitz, Thomas; Frommer, Andreas; Lang, Bruno; Willems, Paul
1
2009
Matrix functions. Zbl 1153.65333
Frommer, Andreas; Simoncini, Valeria
24
2008
Stopping criteria for rational matrix functions of Hermitian and symmetric matrices. Zbl 1203.65079
Frommer, Andreas; Simoncini, Valeria
18
2008
Convergence of stationary iterative methods for Hermitian semidefinite linear systems and applications to Schwarz methods. Zbl 1165.65012
Frommer, Andreas; Nabben, Reinhard; Szyld, Daniel B.
6
2008
An iterative method to compute the sign function of a non-Hermitian matrix and its application to the overlap Dirac operator at nonzero chemical potential. Zbl 1196.65085
Bloch, J.; Frommer, A.; Lang, B.; Wettig, T.
10
2007
Proving the existence of zeros using the topological degree and interval arithmetic. Zbl 1129.65037
Frommer, A.; Hoxha, F.; Lang, B.
2
2007
Extensions of certain graph-based algorithms for preconditioning. Zbl 1149.65033
Fritzsche, David; Frommer, Andreas; Szyld, Daniel B.
1
2007
Existence tests for solutions of nonlinear equations using Borsuk’s theorem. Zbl 1095.47057
Frommer, Andreas; Lang, Bruno
7
2005
Numerical methods for the QCD overlap operator. II: Optimal Krylov subspace methods. Zbl 1077.81528
Arnold, Guido; Cundy, Nigel; van den Eshof, Jasper; Frommer, Andreas; Krieg, Stefan; Lippert, Thomas; Schäfer, Katrin
4
2005
Asynchronous iterations with flexible communication: contracting operators. Zbl 1069.65054
El Baz, Didier; Frommer, Andreas; Spiteri, Pierre
3
2005
Symbolic-numeric techniques for solving nonlinear systems. Zbl 1391.65143
Beelitz, Thomas; Frommer, Andreas; Lang, Bruno; Willems, Paul
2
2005
QCD and numerical analysis III. Proceedings of the third international workshop on numerical analysis and lattice QCD, Edinburgh, UK, June 30 – July 4, 2003. Zbl 1066.81001
2
2005
A comparison of the Moore and Miranda existence tests. Zbl 1069.47060
Frommer, A.; Lang, B.; Schnurr, M.
8
2004
The new nonprobabilistic criterion of failure for dynamical systems based on convex models. Zbl 1112.93038
Qiu, Z. P.; Mueller, P. C.; Frommer, A.
8
2004
On the existence theorems of Kantorovich, Miranda and Borsuk. Zbl 1080.47042
Alefeld, Götz; Frommer, Andreas; Heindl, Gerhard; Mayer, Jan
7
2004
A linear programming based analysis of the CP-rank of completely positive matrices. Zbl 1171.90471
Li, Yingbo; Kummert, Anton; Frommer, Andreas
5
2004
Numerical software with result verification. International Dagstuhl seminar, Dagstuhl Castle, Germany, January 19–24, 2003. Revised papers. Zbl 1046.65001
2
2004
On preconditioners for the Borsuk existence test. Zbl 1354.65098
Frommer, Andreas; Lang, Bruno
2
2004
BiCGStab(\(\ell\)) for families of shifted linear systems. Zbl 1239.65022
Frommer, Andreas
29
2003
Conditions for strict inequality in comparisons of spectral radii of splittings of different matrices. Zbl 1018.65049
Elsner, Ludwig; Frommer, Andreas; Nabben, Reinhard; Schneider, Hans; Szyld, Daniel B.
13
2003
Numerical methods for the QCDd overlap operator. I: Sign-function and error bounds. Zbl 1008.81508
van den Eshof, J.; Frommer, A.; Lippert, Th.; Schilling, K.; van der Vorst, H. A.
27
2002
An algebraic convergence theory for restricted additive and multiplicative Schwarz methods. Zbl 1026.65022
Frommer, A.; Nabben, R.; Szyld, D. B.
3
2002
Algebraic theory of multiplicative Schwarz methods. Zbl 0991.65037
Benzi, Michele; Frommer, Andreas; Nabben, Reinhard; Szyld, Daniel B.
36
2001
An algebraic convergence theory for restricted additive Schwarz methods using weighted max norms. Zbl 1006.65031
Frommer, Andreas; Szyld, Daniel B.
28
2001
An approximate method for the standard interval eigenvalue problem of real non-symmetric interval matrices. Zbl 0991.65040
Qiu, Zhiping; Müller, Peter C.; Frommer, Andreas
7
2001
Stability robustness bounds for linear state-space models with structured uncertainty based on ellipsoidal set-theoretic approach. Zbl 1066.93043
Qiu, Zhiping; Müller, Peter C.; Frommer, Andreas
4
2001
Proving conjectures by use of interval arithmetic. Zbl 0990.65048
Frommer, Andreas
4
2001
Ellipsoidal set-theoretic approach for stability of linear state-space models with interval uncertainty. Zbl 0985.65077
Qiu, Zhiping; Müller, Peter C.; Frommer, Andreas
3
2001
A feasibility result for interval Gaussian elimination relying on graph structure. Zbl 0984.65020
Frommer, Andreas
2
2001
On asynchronous iterations. Zbl 0967.65066
Frommer, Andreas; Szyld, Daniel B.
38
2000
Numerical challenges in lattice quantum chromodynamics. Joint interdisciplinary workshop of John von Neumann Institute for Computing, Jülich, and Institute of Applied Computer Science, Wuppertal Univ., Germany, August 1999. Zbl 0957.00052
20
2000
Weighted max norms, splittings, and overlapping additive Schwarz iterations. Zbl 0934.65035
Frommer, Andreas; Szyld, Daniel B.
36
1999
Fast cg-based methods for Tikhonov–Phillips regularization. Zbl 0943.65068
Frommer, Andreas; Maass, Peter
29
1999
Efficient schemes for nearest neighbor load balancing. Zbl 0942.90023
Diekmann, R.; Frommer, A.; Monien, B.
17
1999
Efficient schemes for nearest neighbor load balancing. Zbl 0930.68163
Diekmann, Ralf; Frommer, Andreas; Monien, Burkhard
3
1999
Optimal and alternating-direction load balancing schemes. Zbl 0947.68008
Elsässer, Robert; Frommer, Andreas; Monien, Burkhard; Preis, Robert
3
1999
A unified approach to parallel space decomposition methods. Zbl 0936.65071
Frommer, Andreas; Renaut, Rosemary A.
2
1999
Parallel space decomposition for minimization of nonlinear functionals. Zbl 0945.65064
Frommer, Andreas; Renaut, Rosemary A.
1
1999
Verified error bounds for linear systems through the Lanczos process. Zbl 1067.65041
Frommer, Andreas; Weinberg, Andre
1
1999
Preconditioning of improved and ”perfect” fermion actions. Zbl 0998.81549
Bietenholz, W.; Eicker, N.; Frommer, A.; Lippert, Th.; Medeke, B.
1
1999
Restarted GMRES for shifted linear systems. Zbl 0912.65023
Frommer, Andreas; Glässner, Uwe
43
1998
Nearest neighbor load balancing on graphs. Zbl 0927.90103
Diekmann, Ralf; Frommer, Andreas; Monien, Burkhard
1
1998
Asynchronous weighted additive Schwarz methods. Zbl 0890.65027
Frommer, Andreas; Schwandt, Hartmut; Szyld, Daniel B.
13
1997
A unified representation and theory of algebraic additive Schwarz and multisplitting methods. Zbl 0892.65017
Frommer, Andreas; Schwandt, Hartmut
12
1997
Scalable parallel SSOR preconditioning for lattice computations in gauge theories. Zbl 0996.68823
Frommer, A.; Lippert, Th.; Schilling, K.
2
1997
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
Asynchronous iterations for enclosing solutions. Zbl 0900.65155
Frommer, A.
1
1996
A comparison result for multisplittings and waveform relaxation methods. Zbl 0831.65031
Frommer, Andreas; Pohl, Bert
11
1995
Asynchronous parallel methods for enclosing solutions of nonlinear equations. Zbl 0837.65051
Frommer, Andreas; Schwandt, Hartmut
3
1995
Asynchronous two-stage iterative methods. Zbl 0821.65010
Frommer, Andreas; Szyld, Daniel B.
29
1994
Comparison results for splittings based on overlapping blocks. Zbl 0819.65038
Frommer, Andreas; Pohl, Bert
1
1994
A new criterion to guarantee the feasibility of the interval Gaussian algorithm. Zbl 0777.65012
Frommer, A.; Mayer, G.
8
1993
Two-stage interval iterative methods. Zbl 0790.65020
Frommer, A.; Mayer, G.
1
1993
Linear systems with \(\Omega\)-diagonally dominant matrices and related ones. Zbl 0774.65013
Frommer, A.; Mayer, G.
1
1993
\(H\)-splittings and two-stage iterative methods. Zbl 0764.65018
Frommer, Andreas; Szyld, Daniel B.
105
1992
On the theory and practice of multisplitting methods in parallel computation. Zbl 0763.65019
Frommer, A.; Mayer, G.
15
1992
Generalized diagonal dominance of nonlinear functions. II: Application to asynchronous iterative methods and examples. (Verallgemeinerte Diagonaldominanz bei nichtlinearen Funktionen. II: Anwendung auf asynchrone Iterationsverfahren und Beispiele.) Zbl 0786.65045
Frommer, A.
2
1992
Asynchronous iterations for enclosing solutions of fixed point problems. Zbl 0838.65061
Frommer, Andreas
1
1992
Generalized diagonal dominance of nonlinear functions. I. (Verallgemeinerte Diagonaldominanz bei nichtlinearen Funktionen. I.) Zbl 0786.65044
Frommer, A.
1
1992
Generalized nonlinear diagonal dominance and applications to asynchronous iterative methods. Zbl 0746.65046
Frommer, Andreas
10
1991
On asynchronous iterations in partially ordered spaces. Zbl 0724.65063
Frommer, Andreas
6
1991
Iterationsverfahren für lineare Gleichungssysteme auf Parallelrechnern. (Iterative methods for systems of linear equations on parallel computers). Zbl 0735.65013
Frommer, A.; Mayer, G.
1
1991
Lösung linearer Gleichungssysteme auf Parallelrechnern. (Solution of systems of linear equations on parallel computers). Zbl 0706.65014
Frommer, Andreas
6
1990
On the R-order of Newton-like methods for enclosing solutions of nonlinear equations. Zbl 0691.65031
Frommer, Andreas; Mayer, Günter
5
1990
Block colouring schemes for the SOR method on local memory parallel computers. Zbl 0699.65020
Block, U.; Frommer, A.; Mayer, G.
5
1990
Theoretische und praktische Ergebnisse zu Multisplitting-Verfahren auf Parallelrechnern. (Theoretical and practical results of multisplitting methods on parallel computers). Zbl 0714.65038
Frommer, A.; Mayer, G.
2
1990
Efficient methods for enclosing solutions of systems of nonlinear equations. Zbl 0721.65025
Frommer, A.; Mayer, G.
2
1990
Convergence of relaxed parallel multisplitting methods. Zbl 0676.65022
Frommer, Andreas; Mayer, Günter
150
1989
Parallel nonlinear multisplitting methods. Zbl 0662.65042
Frommer, Andreas
16
1989
Parallel interval multisplittings. Zbl 0682.65016
Frommer, Andreas; Mayer, Günter
14
1989
Safe bounds for the solutions of nonlinear problems using a parallel multisplitting method. Zbl 0685.65045
Frommer, A.; Mayer, G.
2
1989
Implementing Brown’s method for systems of nonlinear equations with dense banded Jacobian. Zbl 0662.65043
Frommer, A.
1
1989
...and 5 more Documents
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Cited by 1,025 Authors

43 Bai, Zhongzhi
34 Frommer, Andreas
23 Szyld, Daniel B.
20 Huang, Ting-Zhu
14 Zhang, Litao
13 Evans, David John
13 Gu, Tongxiang
12 Mayer, Günter
12 Wang, Deren
12 Zheng, Hua
11 Li, Cuixia
11 Yun, Jae Heon
10 Cao, Zhihao
10 Simoncini, Valeria
10 Wang, Chuanlong
9 Magoulès, Frédéric
9 Miyajima, Shinya
9 Qiu, Zhiping
9 Reichel, Lothar
9 Schweitzer, Marcel
9 Wu, Shiliang
9 Zeng, Jinping
8 Liu, Xingping
8 Liu, Zhongyun
8 Migallón, Violeta
8 Penadés, José
8 Vong, Seakweng
7 Ma, Changfeng
6 Cao, Yang
6 Hladík, Milan
6 Jing, Yanfei
6 Li, Chenliang
6 Li, Wen
6 Song, Yongzhong
6 Vabishchevich, Pëtr Nikolaevich
6 Wang, Xiaojun
6 Zhang, Guofeng
6 Zhang, Lili
5 Carpentieri, Bruno
5 Chen, Xiaojun
5 Dehghan Takht Fooladi, Mehdi
5 Gbikpi-Benissan, Guillaume
5 Gu, Xian-Ming
5 Güttel, Stefan
5 Hashemi, Behnam
5 Kahl, Karsten
5 Mishra, Debasisha
5 Niki, Hiroshi
5 Novati, Paolo
5 Sogabe, Tomohiro
5 Spiteri, Pierre
5 Van Gijzen, Martin Bastiaan
5 Wang, Xiang
5 Wen, Ruiping
5 Yin, Junfeng
4 Aceto, Lidia
4 Bahi, Jacques Mohcine
4 Beckermann, Bernhard
4 Benzi, Michele
4 Brauchart, Johann S.
4 Chang, Dawei
4 Chen, Guoliang
4 Chow, Edmond G. W.
4 Climent, Joan-Josep
4 Cui, Jingjing
4 Franek, Peter
4 Huang, Zhengge
4 Kressner, Daniel
4 Kürschner, Patrick
4 Meng, Guoyan
4 Meng, Jing
4 Miao, Shu-Xin
4 Oh, Seyoung T.
4 Perea, Carmen
4 Sauerwald, Thomas
4 Sun, Zhe
4 Wu, Gang
4 Yang, Haijian
4 Zhang, Shao-Liang
3 Benner, Peter
3 Carstensen, Carsten
3 Chen, Fang
3 Daney, David
3 Dehghani-Madiseh, Marzieh
3 Dong, Junliang
3 Du, Lei
3 El Baz, Didier
3 Elishakoff, Isaac
3 Grimm, Volker
3 Iannazzo, Bruno
3 Jiang, Yingjun
3 Khojasteh Salkuyeh, Davod
3 Kim, Eun Heui
3 Kim, Sangwook
3 Knizhnerman, Leonid
3 Kurbatov, Vitaliĭ Gennad’evich
3 Kurbatova, Irina Vital’evna
3 Landi, Germana
3 Li, Chaoqian
3 Li, Chengliang
...and 925 more Authors
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Cited in 154 Serials

87 Journal of Computational and Applied Mathematics
60 Linear Algebra and its Applications
49 Applied Mathematics and Computation
43 Numerical Algorithms
33 Computers & Mathematics with Applications
30 International Journal of Computer Mathematics
27 SIAM Journal on Scientific Computing
24 Numerical Linear Algebra with Applications
22 Applied Numerical Mathematics
18 Numerische Mathematik
18 SIAM Journal on Matrix Analysis and Applications
14 BIT
12 Computational and Applied Mathematics
11 Linear and Multilinear Algebra
10 Calcolo
10 Computing
10 Applied Mathematics Letters
9 Japan Journal of Industrial and Applied Mathematics
8 Mathematics of Computation
8 Journal of Scientific Computing
7 Computer Methods in Applied Mechanics and Engineering
7 Journal of Computational Physics
7 Journal of Global Optimization
7 Parallel Algorithms and Applications
7 East Asian Journal on Applied Mathematics
6 Advances in Computational Mathematics
6 Mathematical Problems in Engineering
5 Applied Mathematical Modelling
5 Journal of Applied Mathematics and Computing
5 AIMS Mathematics
4 SIAM Journal on Numerical Analysis
4 ETNA. Electronic Transactions on Numerical Analysis
4 Optimization Methods & Software
4 Computational Methods in Applied Mathematics
4 Journal of Applied Mathematics
3 Acta Mechanica
3 Computers and Fluids
3 Computer Physics Communications
3 Journal of Optimization Theory and Applications
3 Mathematics and Computers in Simulation
3 Theoretical Computer Science
3 Acta Mathematicae Applicatae Sinica. English Series
3 Algorithmica
3 Applications of Mathematics
3 Mathematical Programming. Series A. Series B
3 Computational Optimization and Applications
3 Applied Mathematics. Series B (English Edition)
3 Filomat
3 Mediterranean Journal of Mathematics
3 Acta Numerica
2 International Journal of Modern Physics A
2 Journal of Engineering Mathematics
2 Journal of the Franklin Institute
2 Journal of Mathematical Analysis and Applications
2 Nuclear Physics. B
2 Automatica
2 Numerical Functional Analysis and Optimization
2 Results in Mathematics
2 Topology and its Applications
2 Applied Mathematics and Mechanics. (English Edition)
2 Journal of Complexity
2 Discrete & Computational Geometry
2 Journal of Automated Reasoning
2 Computational Mechanics
2 International Journal of Robust and Nonlinear Control
2 The Journal of Analysis
2 Computing and Visualization in Science
2 Journal of Inequalities and Applications
2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
2 Optimization Letters
2 Statistics and Computing
2 Journal of Applied Analysis and Computation
2 Journal of Mathematics
1 Bulletin of the Australian Mathematical Society
1 International Journal of Solids and Structures
1 Inverse Problems
1 Information Processing Letters
1 Journal of Mathematical Physics
1 Journal of Statistical Physics
1 Physics Reports
1 Chaos, Solitons and Fractals
1 Aplikace Matematiky
1 Czechoslovak Mathematical Journal
1 International Journal for Numerical Methods in Engineering
1 Journal of Computer and System Sciences
1 Kybernetika
1 Mathematics of Operations Research
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Mathematica Numerica Sinica
1 Operations Research Letters
1 Graphs and Combinatorics
1 Journal of Symbolic Computation
1 Constructive Approximation
1 International Journal of Parallel Programming
1 Mathematical and Computer Modelling
1 Journal of Applied Mathematics and Stochastic Analysis
1 Signal Processing
1 Computational Statistics
1 Computational Mathematics and Mathematical Physics
1 Aequationes Mathematicae
...and 54 more Serials
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Cited in 40 Fields

669 Numerical analysis (65-XX)
115 Operations research, mathematical programming (90-XX)
107 Linear and multilinear algebra; matrix theory (15-XX)
54 Partial differential equations (35-XX)
45 Computer science (68-XX)
26 Combinatorics (05-XX)
25 Operator theory (47-XX)
21 Mechanics of deformable solids (74-XX)
19 Systems theory; control (93-XX)
17 Ordinary differential equations (34-XX)
17 Quantum theory (81-XX)
15 Fluid mechanics (76-XX)
14 Real functions (26-XX)
14 Approximations and expansions (41-XX)
12 Calculus of variations and optimal control; optimization (49-XX)
8 Statistics (62-XX)
8 Information and communication theory, circuits (94-XX)
6 Functions of a complex variable (30-XX)
6 Integral equations (45-XX)
6 Probability theory and stochastic processes (60-XX)
5 Number theory (11-XX)
5 Algebraic topology (55-XX)
5 Geophysics (86-XX)
5 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
4 Field theory and polynomials (12-XX)
4 Harmonic analysis on Euclidean spaces (42-XX)
4 Mechanics of particles and systems (70-XX)
4 Optics, electromagnetic theory (78-XX)
4 Statistical mechanics, structure of matter (82-XX)
4 Biology and other natural sciences (92-XX)
3 Commutative algebra (13-XX)
3 Special functions (33-XX)
3 Functional analysis (46-XX)
3 General topology (54-XX)
2 Dynamical systems and ergodic theory (37-XX)
2 Integral transforms, operational calculus (44-XX)
1 Mathematical logic and foundations (03-XX)
1 Difference and functional equations (39-XX)
1 Abstract harmonic analysis (43-XX)
1 Differential geometry (53-XX)

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