Research Reports:

Available Reports:

greenpaw New Polynomial Preconditioned GMRES (since renamed to be “Toward Stable and Efficient Polynomial Preconditioned GMRES”) ,  manuscript  2019 (with Jennifer Loe).


greenpaw Polynomial Preconditioned Arnoldi with Stability Control,  SIAM J. Sci. Comput., vol. 43 (2021), pp. A1-A25 (with Mark Embree and Jennifer Loe).


greenpaw Two-grid Deflated Krylov Methods for Linear Equations,  manuscript  2018 (with Zhao Yang ).


greenpaw Perturbed Arnoldi for Computing Multiple Eigenvalues,  manuscript 2016 (with Mark Embree and Thomas Gibson).


greenpaw Weighted Inner Products for GMRES and GMRES-DR, SIAM J. Sci. Comput., vol. 39 (2017), pp. S610-S632, (with Mark Embree and Huy Nguyen).


greenpaw Polynomial Preconditioned BiCGStab and IDR,  manuscript 2016 (with Jennifer Loe).


greenpaw Two-grid and Multiple-grid Arnoldi for Eigenvalues,  SIAM J. Sci. Comput., vol. 40 (2018), pp. A3470–A3494 (with Zhao Yang).


greenpaw New Noise Subtraction Methods in Lattice QCD,  Proceedings of Science,  Vol: Lattice 2016, (2016) 6 pages (with Walter Wilcox and Suman Baral).


greenpaw Pseudoeigenvector Bases and Deflated GMRES for Highly Nonnormal Matrices,  Numer. Linear Alg. Appl.  Applications, 23 (2016), pp. 1032-1045 (with Zhao Yang and Baojiang Zhong).


greenpaw Polynomial Preconditioned GMRES and GMRES-DR, SIAM J. Sci. Comput., 37 (2015), pp. S407-S428 (with Quan Liu and Walter Wilcox).


greenpaw Improved Seed Methods for Symmetric Positive Definite Linear Equations with Multiple Right-hand Sides.  Numer. Linear Alg. Appl., vol. 21,  pp. 453-471, 2014 (with Abdou M. Abdel Rehim and Walter Wilcox).


greenpaw GMRES Convergence for Perturbed Coefficient Matrices, with Application to Approximate Deflation Preconditioning, SIAM. J. Matrix Anal. & Appl., vol. 34 , pp. 1066-1088, 2013 (with Josef A. Sifuentes and Mark Embree).


greenpaw Restarting the Nonsymmetric Lanczos Algorithm for Eigenvalues and Linear Equations Including Multiple Right-Hand Sides, SIAM J. Sci. Comput., vol. 33, pp. 3037-3056, 2011 (with Dywayne Nicely).


greenpaw Deflated and Restarted Symmetric Lanczos Methods for Eigenvalues and Linear Equations with Multiple Right-hand Sides, SIAM J. Sci. Comput., vol. 32, pp. 129-149, 2010 (with Abdou M. Abdel Rehim, Dywayne Nicely and Walter Wilcox).


greenpaw Deflated GMRES for Systems with Multiple Shifts and Multiple Right-Hand Sides, Lin. Alg. Appl., vol. 429, pp. 2415-2434, 2008 (with Dean Darnell and Walter Wilcox).


greenpaw Complementary Cycles of Restarted GMRES, Numer. Linear Alg. Appl., vol. 15, pp. 559-571, 2008, (with Baojiang Zhong).


greenpaw Deflated BiCGStab for linear equations in QCD
problems, Proceedings of Science LAT2007, pp. 026/1-026/7, 2007, (with Abdou M. Abdel-Rehim and Walter Wilcox).


greenpaw Deflated Iterative Methods for Linear Equations with Multiple Right-Hand Sides, Manuscript originally 2004 and since rewritten (with Walter Wilcox).


greenpaw A Harmonic Restarted Arnoldi Algorithm for Calculating Eigenvalues and Determining Multiplicity, Lin. Alg. Appl., vol. 415, pp. 96-113, 2006.


greenpaw Restarted Block GMRES with Deflation of Eigenvalues, Applied Numerical Mathematics, vol. 54, pp. 222-236, 2005.


greenpaw Deflation of Eigenvalues for Iterative Methods in Lattice QCD, Nuclear Physics B (Proc. Suppl.), vol. 129, pp. 856-858, 2004 (with Dean Darnell and Walter Wilcox).


greenpaw Deflation of Eigenvalues for GMRES in Lattice QCD, Nuclear Physics B (Proc. Suppl.), vol. 106, pp. 1067-1069, 2002 (with Walter Wilcox).


greenpaw GMRES with Deflated Restarting. SIAM J. Sci. Comput., vol. 24, pp. 20-37, 2002.


greenpaw Preconditioning Eigenvalues and Some Comparison of Solvers. J. Comp. Appl. Math., vol. 123, pp. 101-116, 2000.


greenpaw Implicitly Restarted GMRES and Arnoldi Methods for Nonsymmetric Systems of Equations. SIMAX, vol. 21, pp. 1112-1135, 2000.


greenpaw Harmonic Projection Methods for Large Nonsymmetric Eigenvalue Problems. Num. Lin. Alg. Appl., vol. 5 pp. 33-55, 1998 (with Min Zeng).


greenpaw On Restarting the Arnoldi Method for Large Nonsymmetric Eigenvalue Problems. Math Comp, vol. 65, pp. 1213-1230, 1996.


greenpaw A Restarted GMRES Method Augmented with Eigenvectors. SIMAX, vol. 16, pp. 1154-1171, 1995.


greenpaw Preconditioning the Lanczos Algorithm for Sparse Symmetric Eigenvalue Problems. SIAM J. Sci. Comput, vol. 14, pp. 585-593, 1993 (with David Scott).


greenpaw Computing Interior Eigenvalues of Large Matrices. Lin Alg Appl, vol. 154/156, pp. 289-309, 1991.


greenpaw Genalizations of Davidson’s Method for Computing Eigenvalues of Sparse Symmetric Matrices. SIAM J. Sci. Stat. Comput, vol. 7, pp. 817-825, 1986 (with David Scott).


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Math Department, Baylor University