## Research Papers of Daniel B. Szyld

(last twenty years or so).

In this page, papers by subject. There is another page with papers in chronological order. Complete list of publications can be found in the CV (Temple format)

1. Krylov subpace iterative methods for linear systems
2. Schwarz methods and domain decomposition
3. Asynchornous parallell methods for linear and nonlinear systems
4. Singular linear systems and Markov chains
5. Reordering techniques to improve the solution of linear systems
6. Other iterative methods for linear systems, including splittings and their properties
7. Matrix properties and applications
8. Eigenvalue problems
9. Solution of Matrix Equations
10. Matrix Funcitons
11. Other papers

### 1. Krylov subpace iterative methods for linear systems

Tania Bakhos, Peter K. Kitanidis, Scott Ladenheim, Arvind K. Saibaba, and Daniel B. Szyld, Multipreconditioned GMRES for Shifted Systems, SIAM Journal on Scientific Computing, vol. 39 (2017) pp. S222-S247. Bibtex

Mian Ilyas Ahmad, Daniel B. Szyld, and Martin B. van Gijzen, Preconditioned multishift BiCG for H2-optimal model reduction, SIAM Journal on Matrix Analysis and Applications, vol. 38 (2016) pp. A668-A690. Bibtex

Chen Greif, Tyrone Rees, and Daniel B. Szyld, GMRES with multiple preconditioners, SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, vol. 74 (2017) pp. 213-231. Bibtex
Software for Multi-preconditioned GMRES available at the Matlab file exchange.

Chen Greif, Tyrone Rees, and Daniel B. Szyld, Additive Schwarz with Variable Weights, Domain Decomposition Methods in Science and Engineering XXI . J. Erhel, M. Gander, L. Halpern, G. Pichot, T. Sassi, and O. Widlund, eds. Lecture Notes in Computer Science and Engineering, Vol. 98, Springer, Berlin and Heidelberg, 2014. Pages 661-668. Bibtex

Kirk M. Soodhalter, Daniel B. Szyld, and Fei Xue, Krylov Subspace Recycling for Sequences of Shifted Linear Systems, Applied Numerical Mathematics, vol. 81 (2014) pp. 105-118. Bibtex

Xiuhong Du, Eldad Haber, Maria Karampataki, and Daniel B. Szyld, Varying Iteration Accuracy Using Inexact Conjugate Gradients in Control Problems governed by PDE's , in Proceedings of the 2nd Annual International Conference on Computational Mathematics, Computational Geometry and Statistics (CMCGS 2013), Ke Chen and C. Raju, eds., Global and Technology Forum, Singapore, 2013, pages 29-38. Bibtex

Xiuhong Du, Marcus Sarkis, Christian E. Schaerer, and Daniel B. Szyld, Inexact and truncated Parareal-in-time Krylov subspace methods for parabolic optimal control problems, Electronic Transactions on Numerical Analysis, vol. 40 (2013) pp. 36-57. Bibtex

Valeria Simoncini and Daniel B. Szyld, On the Superlinear Convergence of MINRES, Numerical Mathematics and Advanced Applications 2011 - Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011, A. Cangiani, R.L. Davidchack, E.H. Georgoulis, A. Gorban, J. Levesley and M.V. Tretyakov, eds. Springer, Berlin and Heidelberg, 2013, pp. 733-740. Bibtex

Hassane Sadok and Daniel B. Szyld, A new look at CMRH and its relation to GMRES, BIT Numerical Mathematics, vol. 52 (2012) pp. 485-501. Bibtex

Mark Embree, Josef A. Sifuentes, Kirk M. Soodhalter, Daniel B. Szyld, and Fei Xue, Short-Term Recurrence Krylov Subspace Methods for Nearly-Hermitian Matrices, SIAM Journal on Matrix Analysis and Applications, vol. 33 (2012) pp. 480-500. Bibtex

Daniel B. Szyld and Fei Xue, Efficient preconditioned inner solves for inexact Rayleigh quotient iteration and their connections to the single-vector Jacobi-Davidson method, SIAM Journal on Matrix Analysis and Applications. vol. 32 (2011) pp. 993-1018. Bibtex

Marlliny Monsalve and Daniel B. Szyld, Inexact Newton with Krylov projection and recycling for Riccati equations Poster presented at the Conference on Numerical Linear Algebra: Perturbation, Performance, and Portability, July 19-20, 2010, Austin, Texas. Bibtex

Valeria Simoncini and Daniel B. Szyld, Interpreting IDR as a Petrov-Galerkin method, SIAM Journal on Scientific Computing, vol. 32 (2010) pp. 1898-1912. Bibtex

Xiuhong Du and Daniel B. Szyld, Inexact GMRES for singular linear systems, BIT Numerical Mathematics, vol. 48 (2008) pp. 511-531. Bibtex

Valeria Simoncini and Daniel B. Szyld, New conditions for non-stagnation of minimal residual methods , Numerische Mathematik, vol. 109 (2008) pp. 477-487. Bibtex

Xiuhong Du and Daniel B. Szyld, A note on the mesh independence of convergence bounds for additive Schwarz preconditioned GMRES Numerical Linear Algebra with Applications, vol. 15 (2008) pp. 547-557. <Bibtex

Marcus Sarkis and and Daniel B. Szyld, Optimal Left and Right Additive Schwarz Preconditioning for Minimal Residual Methods with Euclidean and Energy Norms , Computer Methods in Applied Mechanics and Engineering, vol. 196 (2007) pp. 1612-1621. Bibtex

Valeria Simoncini and Daniel B. Szyld, Recent computational developments in Krylov Subspace Methods for linear systems , Numerical Linear Algebra with Applications, vol. 14 (2007) pp. 1-59. Bibtex

Valeria Simoncini and Daniel B. Szyld, Relaxed Krylov Subspace Approximation, PAMM: Proceedings of Applied Mathematics and Mechanics, vol. 5 (2005) pp. 797-800. Bibtex

Valeria Simoncini and Daniel B. Szyld, The effect of non-optimal bases on the convergence of Krylov Subspace Methods , (Research Report June 2004, revised December 2004). Numerische Mathematik, vol. 100 (2005) pp. 711-733. Journal version. Bibtex

Valeria Simoncini and Daniel B. Szyld, On the Occurrence of Superlinear Convergence of Exact and Inexact Krylov Subspace Methods, SIAM Review, vol. 47 (2005) pp. 247-272. Bibtex

Valeria Simoncini and Daniel B. Szyld, Theory of Inexact Krylov Subspace Methods and Applications to Scientific Computing, in SIAM Journal on Scientific Computing, vol. 25 (2003), pp. 454-477. Bibtex

Valeria Simoncini and Daniel B. Szyld, Flexible Inner-Outer Krylov Subspace Methods, SIAM Journal on Numerical Analysis, vol. 40 (2003), pp. 2219-2239. Bibtex

Daniel B. Szyld and Judith A. Vogel, A Flexible Quasi-Minimal Residual Method with Inexact Preconditioning , SIAM Journal on Scientific Computing, vol. 23 (2001) pp. 363-380. Bibtex

Daniel B. Szyld and Olof B. Widlund, Variational Analysis of Some Conjugate Gradient Methods, East-West Journal of Numerical Mathematics, vol. 1 (1993) 51-74. Bibtex

### 2. Schwarz methods and domain decomposition

José C. Garay Frédéric Magoulès, Daniel B. Szyld, Optimized Schwarz Method for Poisson's Equation in Rectangular Domains, Proceedings of the 24th International Conference on Domain Decomposition Methods. Peter E. Bjostard, Sussane C. Brenner, Lawrence Halpern, Hyea Hyun Kim, Ralf Kornhuber, Talal Rahman, and Olof B. Widlund, eds., Lecture Notes in Computer Science and Engineering, vol. 125, Springer, Berlin and Heidelberg, 2018, pages 533-541. Bibtex

José C. Garay Frédéric Magoulès, Daniel B. Szyld, Convergence of Asynchronous Optimized Schwarz Methods in the plane, Proceedings of the 24th International Conference on Domain Decomposition Methods. Peter E. Bjostard, Sussane C. Brenner, Lawrence Halpern, Hyea Hyun Kim, Ralf Kornhuber, Talal Rahman, and Olof B. Widlund, eds., Lecture Notes in Computer Science and Engineering, vol. 125, Springer, Berlin and Heidelberg, 2018, pages 333-341. Bibtex

Carlos Echeverría, Joerg Liesen, Daniel B. Szyld, and Petr Tichý, Convergence of the multiplicative Schwarz method for singularly perturbed convection-diffusion problems discretized on a Shishkin mesh. Electronic Transactions on Numerical Analysis, vol. 48 (2018) pp.40-62. Bibtex

Sébastien Duminil, Hassane Sadok, and Daniel B. Szyld, Nonlinear Schwarz iterations with Reduced Rank Extrapolation, Research Report 14-09-01, Department of Mathematics, Temple University, September 2014. To appear in Applied Numerical Mathematics. Bibtex

Lahcen Laayouni and Daniel B. Szyld, On the performance of the Algebraic Optimized Schwarz Methods with applications, Numerical Algorithms, vol. 67 (2014) pp. 889-916. Bibtex

Chen Greif, Tyrone Rees, and Daniel B. Szyld, Additive Schwarz with Variable Weights, Domain Decomposition Methods in Science and Engineering XXI . J. Erhel, M. Gander, L. Halpern, G. Pichot, T. Sassi, and O. Widlund, eds. Lecture Notes in Computer Science and Engineering, Vol. 98, Springer, Berlin and Heidelberg, 2014. Pages 661-668. Bibtex

Martin J. Gander, Sébastien Loisel, and Daniel B. Szyld, An optimal block iterative method and preconditioner for banded matrices with applications to PDEs on irregular domains, SIAM Journal on Matrix Analysis and Applications, vol. 33 (2012) pp. 653-680. Bibtex

Olivier Dubois, Martin J. Gander, Sébastien Loisel, Amik St-Cyr, and Daniel B. Szyld, The Optimized Schwarz Method with a Coarse Grid Correction, SIAM Journal on Scientific Computing, vol. 34 (2012) pp. A421-A458. Bibtex

Sébastien Loisel and Daniel B. Szyld, On the geometric convergence of Algebraic Optimized Schwarz Methods with applications to elliptic problems, Research Report 07-11-16, Department of Mathematics, Temple University, November 2007. Numerische Mathematik, vol. 114 (2010) pp. 697-728. Bibtex

Sébastien Loisel and Daniel B. Szyld, On the convergence of Optimized Schwarz Methods by way of Matrix Analysis , Domain Decomposition Methods in Science and Engineering XVIII, Michel Bercovier, Martin Gander, Ralf Kornhuber, and Olof B. Widlund, editors. Lecture Notes in Computational Science and Engineering, Vol. 70, Springer, 2009, pages 363-370. Bibtex

Sébastien Loisel and Daniel B. Szyld, A maximum principle for L2-trace norms with an application to Optimized Schwarz Methods , Domain Decomposition Methods in Science and Engineering XVIII, Michel Bercovier, Martin Gander, Ralf Kornhuber, and Olof B. Widlund, editors. Lecture Notes in Computational Science and Engineering, Vol. 70, Springer, 2009, pages 193-200. Bibtex

Sébastien Loisel, Reinhard Nabben, and Daniel B. Szyld, On hybrid multigrid-Schwarz algorithms , Journal of Scientific Computing, vol. 36 (2008) pp. 165-175. Bibtex

Xiuhong Du and Daniel B. Szyld, A note on mesh independence of convergence bounds for additive Schwarz preconditioned GMRES Numerical Linear Algebra with Applications, vol. 15 (2008) pp. 547-557. Bibtex

Marcus Sarkis and and Daniel B. Szyld, Optimal Left and Right Additive Schwarz Preconditioning for Minimal Residual Methods with Euclidean and Energy Norms , Computer Methods in Applied Mechanics and Engineering, vol. 196 (2007) pp. 1612-1621. Bibtex

Josep Arnal, Violeta Migallón, José Penadés, and Daniel B. Szyld, Newton Additive and Multiplicative Schwarz Iterative Methods , IMA Journal of Numerical Analysis, vol. 28 (2008) pp. 143-161. Bibtex

Reinhard Nabben and Daniel B. Szyld, Schwarz iterations for symmetric positive semidefinite problems , SIAM Journal on Matrix Analysis and Applications. vol. 29 (2006) pp. 98-116. Bibtex

Marcus Sarkis and and Daniel B. Szyld, A Proposal for a Dynamically Adapted Inexact Additive Schwarz Preconditioner, Domain Decomposition Methods in Science and Engineering XVI , Olof Widlund and David Keyes (eds.) Lecture Notes in Computational Science and Engineering, vol. 55, Springer, 2006, pp. 341-345. Bibtex

Rafael Bru, Francisco Pedroche, and Daniel B. Szyld, Additive Schwarz Iterations for Markov Chains , SIAM Journal on Matrix Analysis and Applications, vol. 27 (2005) pp. 445-458. Bibtex

Rafael Bru, Francisco Pedroche, and Daniel B. Szyld, Overlapping Additive and Multiplicative Schwarz Iterations for H-matrices, Linear Algebra and its Applications, vol. 393 (2004), pp. 91-105. Bibtex

Ivo Marek and Daniel B. Szyld, Algebraic Schwarz Methods for the Numerical Solution of Markov Chains, Linear Algebra and its Applications, vol. 386 (2004), pp. 67-81. Bibtex

Reinhard Nabben and Daniel B. Szyld, Convergence theory of restricted multiplicative Schwarz methods, SIAM Journal on Numerical Analysis, vol. 40 (2003), pp. 2318-2336. Bibtex

Andreas Frommer and Daniel B. Szyld, An Algebraic Convergence Theory for Restricted Additive Schwarz Methods Using Weighted Max Norms, SIAM Journal on Numerical Analysis, vol. 39 (2001) pp. 463-479. Bibtex

Michele Benzi, Andreas Frommer, Reinhard Nabben, and Daniel B. Szyld, Algebraic Theory of Multiplicative Schwarz Methods, Numerische Mathematik, vol. 89 (2001) pp. 605-639. Bibtex

Andreas Frommer and Daniel B. Szyld, Weighted Max Norms, Splittings, and Overlapping Additive Schwarz Iterations, Numerische Mathematik, vol. 83 (1999) pp. 259-278. Bibtex

Andreas Frommer, Hartmut Schwandt and Daniel B. Szyld, Asynchronous Weighted Additive Schwarz Methods, Electronic Transaction on Numerical Analysis, vol. 5 (1997) pp. 48-61. Bibtex

### 3. Asynchornous parallell methods for linear and nonlinear systems

Giorgos Kollias, Efstratios Gallopoulos, and Daniel B. Szyld. Asynchronous iterative computations with Web information retrieval structures: The PageRank case. Parallel Computing: Current and Future Issues of High-End Computing (Proceedings of the International Conference Parco05), G.R. Joubert, W.E. Nagel, F.J. Peters, O. Plata, P. Tirado, E. Zapata, eds., John von Neumann-Institut for Computing (NIC), Julich, Germany, NIC Series Volume 33 (ISBN 3-00-017352-8), pages 309-316, 2006. Bibtex

Daniel B. Szyld, Perspectives on Asynchronous Computations for Fluid Flow Problems, Proceedings of the First M.I.T. Conference on Computational Fluid and Solid Mechanics held on June 12 - 14, 2001: Computational Fluid and Solid Mechanics, K.J.Bathe, ed. Elsevier, 2001, pp 977-980. Bibtex

Daniel B. Szyld and Jian-Jun Xu, Convergence of Some Asynchronous Nonlinear Multisplitting Methods , Numerical Algorithms , vol. 25 (2000) pp. 347-361. Bibtex

Andreas Frommer and Daniel B. Szyld, On Asynchronous Iterations, Journal of Computational and Applied Mathematics , vol. 23 (2000) pp. 201-216. Bibtex

Daniel B. Szyld, The Mystery of Asynchronous Iterations Convergence when the Spectral Radius is One, Research Report 98-102, Department of Mathematics, Temple University, October 1998. Bibtex

Andreas Frommer and Daniel B. Szyld, Asynchronous Iterations with Flexible Communication for Linear Systems, Calculateurs Parallèles, Réseaux et Systèmes Répartis, vol. 10 (1998) pp. 421-429. Bibtex

Daniel B. Szyld, Different Models of Parallel Asynchronous Iterations with Overlapping Blocks, Computational and Applied Mathematics, vol. 17 (1998) pp. 101-115. Bibtex

Zhong-Zhi Bai, Violeta Migallón, José Penadés and Daniel B. Szyld, Block and Asynchronous Two-stage Methods for Mildly Nonlinear Systems, Numerische Mathematik, vol. 82 (1999) pp. 1-20. Bibtex

Kostas Blathras, Daniel B. Szyld and Yuan Shi, Timing Models and Local Stopping Criteria for Asynchronous Iterative Algortihms , Journal of Parallel and Distributed Computing, vol. 58 (1999) pp. 446-465. Bibtex

Andreas Frommer, Hartmut Schwandt and Daniel B. Szyld, Asynchronous Weighted Additive Schwarz Methods, Electronic Transaction on Numerical Analysis, vol. 5 (1997) pp. 48-61. Bibtex

### 4. Singular linear systems and Markov chains

Andreas Frommer and Daniel B. Szyld, On Necessary Conditions for Convergence of Stationary Iterative Methods for Hermitian Definite and Semidefinite Linear Systems, Research Report 13-06-11, Department of Mathematics, Temple University, June 2013. Revised Februrary 2014. Bibtex

Andreas Frommer, Reinhard Nabben, and Daniel B. Szyld, Convergence of Stationary Iterative Methods for Hermitian Semidefinite Linear Systems and Applications to Schwarz Methods , SIAM Journal on Matrix Analysis and Applications, vol. 30 (2008) pp. 925-938. Bibtex

David Fritzsche, Volker Mehrmann , Daniel B. Szyld, and Elena Virnik, An SVD approach to identifying meta-stable states of Markov chains, Electronic Transactions on Numerical Analysis (ETNA), vol. 29 (2008) pp. 46-69. Bibtex

Giorgos Kollias, Efstratios Gallopoulos, and Daniel B. Szyld. Asynchronous iterative computations with Web information retrieval structures: The PageRank case. Parallel Computing: Current and Future Issues of High-End Computing (Proceedings of the International Conference Parco05), G.R. Joubert, W.E. Nagel, F.J. Peters, O. Plata, P. Tirado, E. Zapata, eds., John von Neumann-Institut for Computing (NIC), Julich, Germany, NIC Series Volume 33 (ISBN 3-00-017352-8), pages 309-316, 2006. Bibtex

Reinhard Nabben and Daniel B. Szyld, Schwarz iterations for symmetric positive semidefinite problems , SIAM Journal on Matrix Analysis and Applications. vol. 29 (2006) pp. 98-116. Bibtex

Rafael Bru, Francisco Pedroche, and Daniel B. Szyld, Cálculo del Vector PageRank de Google Mediante el método Iterativo de Schwarz (Computation of Google's PageRank Vector with the Schwarz Iterative Method, in Spanish). In Congreso de Métodos Numéricos en Ingeniería 2005. (Proceedings of the Congress on Numerical Methodos in Engeneering, Granada, Spain, July 2005) J.L. Pérez Aparicio et al. (eds.) pp. 263-270. Bibtex

Rafael Bru, Francisco Pedroche, and Daniel B. Szyld, Additive Schwarz Iterations for Markov Chains , SIAM Journal on Matrix Analysis and Applications, vol. 27 (2005) pp. 445-458. Bibtex

Ivo Marek and Daniel B. Szyld, Algebraic Schwarz Methods for the Numerical Solution of Markov Chains, Linear Algebra and its Applications, vol. 386 (2004) pp. 67-81. Bibtex

Daniel B. Szyld and Ivo Marek, Comparison of Convergence of General Stationary Iterative Methods for Singular Matrices, SIAM Journal on Matrix Analysis and Applications, vol. 24 (2002) pp. 68-77. Bibtex

Daniel B. Szyld and Ivo Marek, Comparison Theorems for the Convergence Factor of Iterative Methods for Singular Matrices, Linear Algebra and its Applications, vol. 316 (2000) pp. 67-87. Bibtex

Violeta Migallón, José Penadés and Daniel B. Szyld, Experimental Study of Parallel Iterative Solutions of Markov Chains with Block Partitions, Research Report 99-2-10, Department of Mathematics, Temple University, Febrauary 1999. Appeared (in revised form) in Numerical Solutions of Markov Chains (NSMC'99), Brigitte Plateau, William J. Stewart, and Manuel Silva, eds., Prensas Universitarias de Zaragoza, 1999, pp. 96-110. Bibtex

Michele Benzi and Daniel B. Szyld, Existence and Uniqueness of Splittings for Stationary Iterative Methods with Applications to Alternating Methods, Numerische Mathematik vol. 76 (1997) pp. 309-321. Bibtex See also earlier report.

Hwajeong Choi and Daniel B. Szyld, Application of Threshold Partitioning of Sparse Matrices to Markov Chains, Proceedings of the IEEE International Computer Performance and Dependability Symposium IPDS'96, pages 158-165, September 1996. Bibtex

Violeta Migallón, José Penadés and Daniel B. Szyld, Block Two-stage Methods for Singular Systems and Markov Chains, Research Report 95-121, Department of Mathematics, Temple University, December 1995. This paper appeared, in revised form, in Numerical Linear Algebra with Applications, vol. 3 (1996) pp. 413-426. Bibtex

Daniel B. Szyld, Equivalence of Convergence Conditions for Iterative Methods for Singular Equations, Numerical Linear Algebra with Applications, vol. 1 (1994) 151-154. Bibtex

Ivo Marek and Daniel B. Szyld, Local convergence of the (exact and inexact) iterative aggregation method for linear systems and Markov operators, Numerische Mathematik, vol. 693 (1994) pp. 61-82.

Ivo Marek and Daniel B. Szyld, Iterative and Semi-iterative Methods for Computing Stationary Probability Vectors of Markov Operators, Mathematics of Computation, vol. 61 (1993) 719-731.

### 5. Reordering techniques to improve the solution of linear systems

David Fritzsche, Andreas Frommer, Stephen Shank , and Daniel B. Szyld, Overlapping blocks by growing a partition with applications to preconditioning, SIAM Journal on Scientific Computing, vol. 35 (2013) pp. A453-A473. Bibtex

David Fritzsche, Andreas Frommer, and Daniel B. Szyld, Extensions of Certain Graph-based Algorithms or Preconditioning , SIAM Journal on Scientific Computing, vol. 29 (2007) pp. 2144-2161. Bibtex

Michele Benzi, Daniel B. Szyld, and Arno van Duin, Orderings for Incomplete Factorization Preconditioning of Nonsymmetric Problems, SIAM Journal on Scientific Computing vol. 20 (1999) pp. 1652-1670. Bibtex

Michele Benzi, Hwajeong Choi and Daniel B. Szyld, Threshold Ordering for Preconditioning Nonsymmetric Problems, Scientific Computing, Proceedings of the Workshop, 10-12 March 1997, Hong Kong, Springer, Singapore, 1997. pages 159-165. Bibtex

Hwajeong Choi and Daniel B. Szyld, Application of Threshold Partitioning of Sparse Matrices to Markov Chains, Proceedings of the IEEE International Computer Performance and Dependability Symposium IPDS'96, pages 158-165, September 1996. Bibtex

### 6. Other iterative methods for linear systems, including splittings and their properties

Andreas Frommer and Daniel B. Szyld, On Necessary Conditions for Convergence of Stationary Iterative Methods for Hermitian Semidefinite Linear Systems, Linear Algebra and its Applications, vol. 453 (2014) pp. 192-201. Bibtex

Andreas Frommer, Reinhard Nabben, and Daniel B. Szyld, Convergence of Stationary Iterative Methods for Hermitian Semidefinite Linear Systems and Applications to Schwarz Methods , SIAM Journal on Matrix Analysis and Applications, vol. 30 (2008) pp. 925-938. Bibtex

Ludwig Elsner, Andreas Frommer, Reinhard Nabben, Hans Schneider, and Daniel B. Szyld, Conditions for strict inequality in comparisons of spectral radii of splittings of different matrices, Linear Algebra and its Applications, vol. 363 (2003) pp. 65-80. Bibtex

Violeta Migallón, José Penadés, and Daniel B. Szyld, Nonstationary Multisplittings with General Weighting Matrices, SIAM Journal on Matrix Analysis and Applications, vol. 22 (2001) pp. 1089-1094. Bibtex

Michele Benzi and Daniel B. Szyld, Existence and Uniqueness of Splittings for Stationary Iterative Methods with Applications to Alternating Methods, Numerische Mathematik, vol. 76 (1997) pp. 309-321. Bibtex See also earlier report.

### 7. Matrix properties and applications

Bryan Shader, Naomi Shaked-Monderer, and Daniel B. Szyld, Nearly positive matrices, Linear Algebra and its Applications, vol. 449 (2014) pp. 520-544. Bibtex

Abed Elhashash and Daniel B. Szyld, Matrix functions preserving sets of generalized nonnegative matrices, Electronic Journal of Linear Algebra. vol. 20 (2010) pp. 673-690. Bibtex

Valeria Simoncini and Daniel B. Szyld, On the field of values of oblique projections, Linear Algebra and its Applications, vol. 433 (2010) pp. 810-818. Bibtex

Abed Elhashash, Uriel G. Rothblum, and Daniel B. Szyld, Paths of matrices with the strong Perron-Frobenius property converging to a given matrix with the Perron-Frobenius property, the Electronic Journal of Linear Algebra, vol. 19 (2009) pp. 90-97. Bibtex

Abed Elhashash and Daniel B. Szyld, Two Characterizations of Matrices with the Perron-Frobenius Property, Numerical Linear Algebra with Applications, vol. 16 (2009) pp. 863-869. Bibtex
Part of the material of this paper comes from: Perron-Frobenius Properties of General Matrices, Research Report 07-01-10, Department of Mathematics, Temple University, January 2007 (Revised November 2007). Bibtex

Abed Elhashash and Daniel B. Szyld, Generalizations of M-matrices which may not have a nonnegative inverse, Linear Algebra and its Applications, vol. 249 (2008) pp. 2435-2450. Bibtex

Abed Elhashash and Daniel B. Szyld, On general matrices having the Perron-Frobenius property, Electronic Journal of Linear Algebra, vol. 17 (2008) pp. 389-413. Bibtex
Part of the material of this paper comes from: Perron-Frobenius Properties of General Matrices, Research Report 07-01-10, Department of Mathematics, Temple University, January 2007. Bibtex
Video of a talk on Matrices with Perron-Frobenius Properties" at the Workshop on Theoretical and Applied Aspects of Nonnnegative Matrices at the Banff International Research Station for Mathematical Innovation and Discovery, Banff, Alberta, Canada, 27-29 July 2012.

Rafael Bru, Francisco Pedroche, and Daniel B. Szyld, Subdirect Sums of S-Strictly Diagonally Dominant Matrices, Electronic Journal of Linear Algebra
, vol. 15 (2006) pp. 201-209. Bibtex

Daniel B. Szyld, The Many Proofs of an Identity on the Norm of Oblique Projections , Numerical Algorithms, vol. 42 (2006) pp. 309-323. Bibtex

Rafael Bru, Francisco Pedroche, and Daniel B. Szyld, Subdirect sums of nonsingular M-matrices and of their inverses , Electronic Journal of Linear Algebra, vol. 13 (July 2005) pp. 162-174. Bibtex

Paul J. Lanzkron, Donald J. Rose, and Daniel B. Szyld, Convergence of nested classical iterative methods for linear systems, Numerische Mathematik, vol. 58 (1991) pp. 685-702. Bibtex

### 8. Eigenvalue problems

Daniel B. Szyld and Fei Xue, Preconditioned eigensolvers for large-scale nonlinear Hermitian eigenproblems with variational characterizations. I. Conjugate gradient methods, Research Report 14-08-26, Department of Mathematics, Temple University, August 2014. Bibtex

Daniel B. Szyld and Fei Xue, Local convergence of Newton-like methods for degenerate eigenvalues of nonlinear eigenproblems, Research Report 12-10-04, Department of Mathematics, Temple University, October 2012. Published in revised form in two parts:
Part I. Classical Algorithms. Numerische Mathematik, vol. 129 (2015), pp. 353-381. Bibtex
Part II. Accelerated algorithms.
Numerische Mathematik, vol. 129 (2015), pp. 382-403. Bibtex

Daniel B. Szyld and Fei Xue, Several properties of invariant pairs of nonlinear algebraic eigenvalue problems, IMA Journal of Numerical Anlysis. vol. 34 (2014), pp. 921-954. Bibtex

Daniel B. Szyld and Fei Xue, Local convergence analysis of several inexact Newton-type algorithms for general nonlinear eigenvalue problems, Numerische Mathematik, vol. 123 (2013) pp. 333-362. Bibtex

Daniel B. Szyld and Fei Xue, Efficient preconditioned inner solves for inexact Rayleigh quotient iteration and their connections to the single-vector Jacobi-Davidson method, SIAM Journal on Matrix Analysis and Applications. vol. 32 (2011) pp. 993-1018. Bibtex

### 9. Solution of Matrix Equations

Stephen D. Shank, Valeria Simoncini, and Daniel B. Szyld, Efficient low-rank solutions of generalized Lyapunov equations, Research Report 14-11-10, Department of Mathematics, Temple University, November 2014. Bibtex

Valeria Simoncini, Daniel B. Szyld, and Marlliny Monsalve, On the numerical solution of large-scale Riccati equations, IMA Journal of Numerical Anlysis. vol. 34 (2014), pp. 904-920. Bibtex

Marlliny Monsalve and Daniel B. Szyld, Inexact Newton with Krylov projection and recycling for Riccati equations Poster presented at the Conference on Numerical Linear Algebra: Perturbation, Performance, and Portability, July 19-20, 2010, Austin, Texas. Bibtex

### 10. Matrix Functions

Andreas Frommer, Kathryn Lund, and Daniel B. Szyld, Block Krylov subspace methods for functions of matrices, Electronic Transactions on Numerical Analysis, vol. 47 (2017) pp. 100-126. Bibtex
Software avalable at Gitlab

Andreas Frommer, Kathryn Lund, Marcel Schweitzer, and Daniel B. Szyld, The Radau-Lanczos method for matrix functions, SIAM Journal on Matrix Analysis and Applications, vol. 38 (2017) pp. 710-732. Bibtex

### 10. Other papers

Xingwei Yang, Daniel B. Szyld, and Longin Jan Latecki, Diffusion on a Tensor Product Graph for Semi-Supervised Learning and Interactive Image Segmentation, Advances in Imaging and Electron Physics, vol. 169 (2011) pp. 147-172. Bibtex

More Papers.

Work on many of these papers was supported in part by the Department of Energy, and by the National Science Foundation.

There is another page with papers in chronological order. Complete list of publications can be found in the CV (Temple format)