Matrix functions and nonlinear matrix equations

• An Arbitrary Precision Scaling and Squaring Algorithm for the Matrix Exponential (with M. Fasi). SIAM J. Matrix Anal. Appl., 40(4):1233-1256, 2019.
• Computing the Wave-Kernel Matrix Functions (with P. Nadukandi). SIAM J. Sci. Comput., 40(6):A4060-A4082, 2018. MATLAB software.
• Multiprecision Algorithms for Computing The Matrix Logarithm (with Massimiliano Fasi). SIAM J. Matrix Anal. Appl., 39(1):472-491, 2018.
• Computing the Action of Trigonometric and Hyperbolic Matrix Functions (with Peter Kandolf), SIAM J. Sci. Comput., 39(2):A613-A627, 2017.
• An Algorithm to Compute the Polar Decomposition of a 3x3 Matrix (with Vanni Noferini ) Numer. Algorithms, 73(2):349-369, 2016. MATLAB codes on GitHub.
• Matching Exponential-Based and Resolvent-Based Centrality Measures (with Mary Aprahamian and Des Higham), Journal of Complex Networks, 4(2):157-176, 2016.
• A Catalogue of Software for Matrix Functions. Version 2.0 (with Edvin Deadman), MIMS EPrint 2016.3, January 2016; updated March 2016.
• Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms (with Mary Aprahamian ), SIAM J. Matrix Anal. Appl., 37(4):1453-1477, 2016. MATLAB codes on GitHub.
• Ranking the Importance of Nuclear Reactions for Activation and Transmutation Events (with Wayne Arter, J. Guy Morgan and Samuel Relton) Nuclear Science and Engineering, 184(4):561-574, 2016.
• Testing Matrix Function Algorithms Using Identities (with Edvin Deadman), ACM Trans. Math. Soft., 42(1):4:1-4:15, 2016. MATLAB codes on GitHub.
• New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously (with Awad Al-Mohy and Samuel Relton), SIAM J. Sci. Comp., 37(1): A456-A487, 2015. MATLAB codes on Github and MATLAB Central File Exchange.
• An Algorithm for the Matrix Lambert W Function (with Massimiliano Fasi and Bruno Iannazzo), SIAM J. Matrix Anal. Appl., 36(2): 669-685, 2015. MATLAB code.
• Matrix Functions: Computation In Encyclopedia of Applied and Computational Mathematics, B. Engquist, editor, Springer-Verlag, Berlin, 2015, pages 863-865.
• Estimating the Condition Number of the Fréchet Derivative of a Matrix Function (with Samuel Relton), SIAM J. Sci. Comp., 36(6):C617-C634, 2014.
• Higher Order Fréchet Derivatives of Matrix Functions and the Level-2 Condition Number (with Samuel Relton ), SIAM J. Matrix Anal. Appl., 35(3):1019-1037, 2014.
• Functions of Matrices, In Handbook of Linear Algebra, Leslie Hogben, (ed), Second edition, Chapman and Hall/CRC, Boca Raton, FL, USA, 17.1-17.5: 2014.
• The Matrix Unwinding Function, with an Application to Computing the Matrix Exponential (with Mary Aprahamian ), SIAM J. Matrix Anal. Appl. 35 (1): 88-109, 2014. MATLAB codes.
• An Improved Schur-Padé Algorithm for Fractional Powers of a Matrix and their Fréchet Derivatives (with Lijing Lin), SIAM J. Matrix Anal. Appl. 34 (3): 1341-1360, 2013. MATLAB codes at MATLAB Central File Exchange;
• Computing the Fréchet Derivative of the Matrix Logarithm and Estimating the Condition Number (with Awad Al-Mohy and Samuel Relton), SIAM J. Sci. Comp. 35 (4), C394-C410, 2013. MATLAB codes at MATLAB Central File Exchange;
• Blocked Schur Algorithms for Computing the Matrix Square Root (with Edvin Deadman and Rui Ralha), In P. Manninen and P. Öster, eds, Applied Parallel and Scientific Computing: 11th International Conference, PARA 2012, Helsinki, Finland, Lecture Notes in Computer Science, Vol 7782, pp, 171-182, Springer, 2013.
• Backward Stability of Iterations for Computing the Polar Decomposition (with Yuji Nakatsukasa), SIAM J. Matrix Anal. Appl. 33(2):460-479, 2012.
• Improved Inverse Scaling and Squaring Algorithms for the Matrix Logarithm (with Awad Al-Mohy), SIAM J. Sci. Comp. 34 (4): C152-C169, 2012. MATLAB codes. MATLAB codes at MATLAB Central File Exchange.
• A Schur-Padé Algorithm for Fractional Powers of a Matrix (with Lijing Lin), SIAM J. Matrix Anal. Appl. 32(3):1056-1078, 2011. MATLAB codes. MATLAB codes at MATLAB Central File Exchange.
• Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators (with Awad Al-Mohy), SIAM J. Sci. Comp. 33 (2): 488-511, 2011. MATLAB codes. MATLAB codes at MATLAB Central File Exchange.
• On pth Roots of Stochastic Matrices (with Lijing Lin), Linear Algebra Appl. 435(3):448-463, 2011. Published version.
• Computing Matrix Functions (with Awad Al-Mohy), Acta Numerica 19: 159-208, 2010.
• The Canonical Generalized Polar Decomposition (with Christian Mehl and Françoise Tisseur), SIAM J. Matrix Anal. Appl. 31(4): 2163-2180, 2010.
• The Complex Step Approximation to the Fréchet Derivative of a Matrix Function (with Awad Al-Mohy), Numer. Alg. 53(1): 133-148, 2010. Published version.
• The Scaling and Squaring Method for the Matrix Exponential Revisited, SIAM Review 51(4): 747-764, 2009.
• A New Scaling and Squaring Algorithm for the Matrix Exponential (with Awad Al-Mohy), SIAM J. Matrix Anal. Appl. 31(3): 970-989, 2009. MATLAB codes.
• Computing the Fréchet Derivative of the Matrix Exponential, with an Application to Condition Number Estimation (with Awad Al-Mohy), SIAM J. Matrix Anal. Appl. 30(4): 1639-1657, 2009.
• Computing $A^\alpha$, $\log(A)$ and Related Matrix Functions by Contour Integrals (with Nicholas Hale and Lloyd N. Trefethen), SIAM J. Numer. Anal. 46 (5):2505-2523, 2008.
• The solution of S exp(S) = A is not always the Lambert W function of A (with R. M. Corless, H. Ding, and D. J. Jeffrey), ISSAC '07: Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation, pages 116-121. ACM Press, New York, 2007.
• Iterative Solution of a Nonsymmetric Algebraic Riccati Equation (with Chun-Hua Guo ), SIAM J. Matrix Anal. Appl., 29(2):396-412, 2007.
• Functions of Matrices , in Handbook of Linear Algebra, edited by L. Hogben, Chapman and Hall/CRC, Boca Raton, FL, USA, pages 11.1-11.13, 2006.
• A Schur-Newton Method for the Matrix p'th Root and its Inverse (with Chun-Hua Guo ), SIAM J. Matrix Anal. Appl., 28(3):788-804, 2006.
• Efficient Algorithms for the Matrix Cosine and Sine (with Gareth Hargreaves), Numerical Algorithms, 40(4):383-400, 2005.
• Functions Preserving Matrix Groups and Iterations for the Matrix Square Root (with D. Steven Mackey, Niloufer Mackey and Françoise Tisseur), SIAM J. Matrix Anal. Appl., 26(3):849-877, 2005.
• The Scaling and Squaring Method for the Matrix Exponential Revisited, SIAM J. Matrix Anal. Appl., 26(4):1179-1193, 2005.
• Algorithms for the Matrix p'th Root (with Dario A. Bini and Beatrice Meini ), Numerical Algorithms, 39(4):349-378, 2005.
• Computing f(A)b for Matrix Functions f (with Philip Davies). In A. Borici, A. Frommer, B. Joo, A. Kennedy, and B. Pendleton, editors, QCD and Numerical Analysis III , volume 47 of Lecture Notes in Computational Science and Engineering, pages 15-24. Springer-Verlag, Berlin, 2005.
• Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups (With D. Steven Mackey, Niloufer Mackey and Françoise Tisseur ), SIAM J. Matrix Anal. Appl., 25(4):1178-1192, 2004.
• J-Orthogonal Matrices: Properties and Generation , SIAM Review, 45(3), 504-519, 2003.
• Computing the Matrix Cosine (with Matthew I. Smith), Numerical Algorithms, 34:13-26, 2003.
• A Schur-Parlett Algorithm for Computing Matrix Functions (with Philip Davies), SIAM J. Matrix Anal. Appl., 25(2):464-485, 2003.
• Solving a Quadratic Matrix Equation by Newton's Method with Exact Line Searches (with Hyun-Min Kim), SIAM J. Matrix Anal. Appl., 23(2): 303-316, 2001.
• Evaluating Padé Approximants of the Matrix Logarithm , SIAM J. Matrix Anal. Appl. 22(4): 1126-1135, 2001.
• Approximating the Logarithm of a Matrix to Specified Accuracy with Sheung Hun Cheng, Charles S. Kenney and Alan J. Laub), SIAM J. Matrix Anal. Appl. 22(4): 1112-1125, 2001.
• Numerical Analysis of a Quadratic Matrix Equation (with Hyun-Min Kim), IMA J. Numer. Anal., 20(4): 499-519, 2000.
• Return to the Middle Ages: A Half-Angle Iteration for the Logarithm of a Unitary Matrix , (with Sheung Hun Cheng, Charles S. Kenney, Alan J. Laub), Proceedings of the Fourteenth International Symposium of Mathematical Theory of Networks and Systems, Perpignan, France, 2000.
• A New sqrtm for MATLAB , NA Report 336, January 1999.
• Stable Iterations for the Matrix Square Root , Numerical Algorithms, 15(2): 227-242, 1997.
• A Parallel Algorithm for Computing the Polar Decomposition (with Pythagoras Papadimitriou), Parallel Computing, 20(8):1161-1173, Aug. 1994.
• The Matrix Sign Decomposition and its Relation to the Polar Decomposition , Linear Algebra and Appl., 212/213:3-20, 1994.
• Fast polar decomposition of an arbitrary matrix (with R. S. Schreiber), SIAM J. Sci. Stat. Comput., 11(4):648-655, July 1990.
• Newton's Method for the Matrix Square Root , Math. Comp., 46(174):537-549, 1986. At MIMS Eprints .
• Computing Real Square Roots of a Real Matrix , Linear Algebra and Appl., 88/89:405-430, 1987. At MIMS Eprints .
• Computing the Polar Decomposition---with Applications , SIAM J. Sci. Stat. Comput., 7(4):1160-1174, 1986.