Research Reports:

Available Reports:

greenpaw New Polynomial Preconditioned GMRES,  manuscript  2019 (with Jennifer Loe).

NewPPGMRES

greenpaw Polynomial Preconditioned Arnoldi,  manuscript  2018 (with Mark Embree and Jennifer Loe).

PPArn

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

2GridLE

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

PertArnMEV

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

GWeighted

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

PPNonSymmLancLinEqs

greenpaw Two-grid and Multiple-grid Arnoldi for Eigenvalues,  a modified version has been accepted by SIAM J. Sci. Comput. (2018)  (with Zhao Yang).

MGArnoldi

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

NoiseSub

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).

psevects

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

ppgmres

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).

seed

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).

StabGMRES

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).

nlandr

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).

landr

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).

gshift

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

ccyc

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).

Dbicgstab

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

gproj

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

harmArn

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

bgdr

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).

Lat2004

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

qcd

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

gmresdr

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

pre-evals

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

GMRES-IR

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

ien

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

Arnoldi96

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

GMRES-E

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

PL

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

InterEvals

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).

GD

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Math Department, Baylor University