Publications:

Theoretical Comparison of two-level preconditioners based on multigrid and deflation
jointly with J.M. Tang, S.P. MacLachlan and C.. Vuik, SIAM Journal on Matrix Analysis and Applications 31, 1715-1739, (2010)




On a multilevel Krylov method for the Helmholtz equation preconditioned by the shifted Laplacian
jointly with Y. A. Erlangga, ETNA, Vol. 31, 403--424, (2008)




On the Factorization of Simplex Basis Matrices
jointly with R. Luce, J. Duintjer Tebbens, M. Groetschel, T. Koch, J. Liesen and O. Schenk, Zuse Institute Berlin, ZIB-Report 09-24, 2009




Comparison of two-level preconditioners derived from Deflation, Domain Decomposition and Multigrid Methods
jointly with J.M. Tang, K. Vuik,Y. A. Erlangga, Journal on Scientific Computing, Vol. 39, 340--370, (2009)




Theoretical and Numerical Comparison of Various Projection Methods derived from Deflation, Domain Decomposition and Multigrid Methods (extended version)
jointly with J.M. Tang, K. Vuik,Y. A. Erlangga,




Convergence of Stationary Iterative Methods for Hermitian Semidefinite Linear Systems and Applications to Schwarz Methods
jointly with A. Frommer and D.B. Szyld, SIAM Journal on Matrix Analysis and Applications, Vol. 30, 925--938, (2008)




Multilevel projection-based nested Krylov iterations for boundary value problems
jointly with Y. A. Erlangga, SIAM Journal on Scientific Computing, Vol. 30, 1572--1595, (2008)




On algebraic multilevel methods for non-symmetric systems - comparison results
jointly with C. Mense, Linear Algebra and its Applications, Vol. 429, 2567--2588, (2008)




On algebraic multilevel methods for non-symmetric systems - convergence results
jointly with C. Mense, ETNA, Vol. 30, 323--345, (2008)




Deflation and balancing preconditioners for Krylov subspace methods applied to nonsymmetric matrices
jointly with Y. A. Erlangga, SIAM Journal on Matrix Analysis and Applications, 30, 165-175, (2008)




On hybrid multigrid-Schwarz algorithms
jointly S. Loisel and D.B. Szyld, Journal on Scientific Computing, 36, 165-175, (2008)




A comparison of Deflation, Balancing and additive coarse grid correction
jointly with C. Vuik, Numerical Linear Algebra with Applications, 15, 355-372, (2008)




Generalisation of the Perron-Frobenius theory to matrix pencils
jointly with V. Mehrmann and E. Virnik, Linear Algebra and its Applications, Vol. 428 , 20-38, 2007




On relationships between several classes of Z-matrices, M-matrices and nonnegative matrices,
Linear Algebra and its Applications, Vol. 421 (2-3), 417-439, 2007




Domain Decomposition methods and deflated Krylov subspace iterations
jointly with C. Vuik, European Conference on Computational Fluid Dynamics ECCOMAS CFD 2006 editors: P. Wesseling, E. Onate and J. Periaux TU Delft, Delft, 2006 CDROM ISBN 90-9020970-0




Schwarz Iterations for symmetric positive semidefinte problems
jointly with D. Szyld, SIAM Journal on Matrix Analysis and Applications, Vol. 29, 98-116, 2006 .




Deflation acceleration for domain decomposition preconditioners
jointly with C. Vuik and J. Tang, Proceedings of the 8th European Multigrid Conference September 27-30, 2005 Scheveningen The Hague, The Netherlands editors: P. Wesseling, C.W. Oosterlee, P. Hemker TU Delft, Delft, 2006 CDROM ISBN 90-9020969-7




A comparison of Deflation and the Balancing Neumann-Neumann preconditioner
jointly with C. Vuik, SIAM Journal on Scientific Computing 27, 8, 1742-1759, (2006)




A comparison of Deflation and Coarse Grid Correction methods with application in porous media problems,
jointly with C. Vuik, SIAM Journal on Numerical Analysis, 42, 4, 1631-1647, (2004)




Comparisons between additive and multiplicative Schwarz iterations in domain decomposition methods
Numerische Mathematik 95, 145-162, (2003)




Convergence theory of restricted multiplicative Schwarz methods
SIAM Journal on Numerical Analysis, 40, 2318--2336 (2003), jointly with D.B. Szyld




An Algebraic Convergence Theory for Restricted Additive and Multiplicative Schwarz Methods
Proceedings of the 13th International Conference on Domain Decomposition Methods in Lyon, France, 369-375, 2001, jointly with A. Frommer, and D.B. Szyld
 

Conditions for strict inequality in comparisons of spectral radii of splittings of different matrices
Linear Algebra and its Applications, 363, 65--80, (2003) jointly with L. Elsner, A. Frommer, D.B. Szyld, and H. Schneider
 

Algebraic theory of multiplicative Schwarz methods
Numerische Mathematik 89:605-639 (2001), jointly with M. Benzi, A. Frommer, and D.B. Szyld
 

On Cheeger-type inequalities for weighted graphs
Journal of Graph Theory 41, 1--17, (2002), jointly with S. Friedland
 

On Green's matrices of Trees
SIAM J. Matrix Anal. Appl. 22 No. 4 (2000), 1014 - 1026
 

Improved upper bounds for the real part of nonmaximal eigenvalues of nonnegative matrices,
SIAM J. Matrix Anal. Appl. 22 No. 2 (2000), 574- 579
 

A class of inverse M-matrices
The ELECTRONIC Journal of LINEAR ALGEBRA 7 (2000) 53-58
 

On Decay Rates of Tridiagonal and Band Matrices,
SIAM J. Matrix Anal. Appl. 20 (1999) 820-837
 

Some properties of the block matrices in the parallel decomposition-type relaxation methods,
Applied Numerical Mathematics, 29 (1999) 167-170, jointly with Z.-Z. Bai,
 

Two-sided bounds on the inverse of diagonally dominant tridiagonal matrices,
Lin. Alg. Appl. 287 (1999) 289-305,
 

Orthogonal Basis Which Lead to Symmetric Nonnegative Matrices,
Lin. Alg. Appl., 271 (1998) 323--343) jointly with L. Elsner and M. Neumann.
 

Inverse Tridiagonal Z-matrices,
Lin. Mult. Alg. 45 (1998) 75--97, jointly with J.J. McDonald, M. Neumann, M. Tsatsomeros, and H. Schneider
 

Matrices whose Inverse is a generalized M-matrix,
Lin. Mult. Alg. 44 (1998) 67--84.
 

On the second real eigenvalue of nonnegative and Z-matrices,
Lin. Alg. Appl. 255 (1997) 303-313, jointly with S. Friedland
 

Z-matrices and Inverse Z-matrices,
Lin. Alg. Appl. 256 (1997) 31-48.
 

A Characterization of M-matrices,
SFB 343 Preprint 95-002, 1995.
 

On classes of inverse Z-matrices,
Lin. Alg. Appl. 223/224 (1995) 521-55, jointly with R.S. Varga.
 

Generalized ultrametric matrices - a Class of Inverse M-matrices,
Lin. Alg. Appl. 220 (1995) 365-390, jointly with R.S. Varga.
 

A Note on Comparison Theorems of Splittings and Multisplittings of Hermitian positive definite Matrices,
Lin. Alg. Appl. 233 (1996) 67-80.
 

A linear algebra proof that the inverse of a strictly ultrametric matrix is a strictly diagonally dominant Stieltjes matrix,
SIAM J. Matrix Analysis and Appl. 15(1994), 107-113, jointly with R.S. Varga.
 

An algorithm for determining if the inverse of a strictly diagonally dominant Stieltjes matrix is strictly ultrametric,
Numerische Mathematik 65, 493-501 (1993), jointly with R.S. Varga.
 

On symmetric ultrametric matrices,
in Numerical Linear Algebra, (L. Reichel, A. Ruttan, R.S. Varga, eds.) Walter de Gruyter, New York (1993), 193-199, jointly with R.S. Varga.
 

A new application for generalized M-matrices,
in Numerical Linear Algebra, (L. Reichel, A. Ruttan, R.S. Varga, eds.) Walter de Gruyter, New York (1993), 179-193.
 

On a class of matrices which arise in the numerical solution of Euler equations,
Numerische Mathematik, 63, 411-431 (1992).
 

Konvergente Iterationsverfahren für unsymmetrische Blockmatrizen,
Dissertation, Universität Bielefeld, 1991.