Preprints.

Here you can find recent works of mine. The date shown close to works refers to the latest date of modification of the work.
Author: Luca Dieci < dieci@math.gatech.edu>

These preprints are provided to you "as they are". I will be glad to hear from you if you have comments on these works.

I appreciate it if you avoid plagiarizing these works, and if you quote them in any work of yours which make use of them. Thanks.

Finally, I gratefully acknowledge the support of the National Science Foundation (NSF) during the time period in which these works were written.

Orthonormal integrators based on Householder and Givens transformations [Appeared in FGCS: Future Generation Computer Systems -- Computational Science].

Lyapunov exponents of systems evolving on quadratic groups [Appeared in SIAM J. Matrix Analysis and Applications].

Smooth SVD on the Lorentz group with application to computation of Lyapunov exponents [Appeared in J.Comput. Appl. Math.].

Jacobian free computation of Lyapunov exponents [Appeared in J. Dynamics and Differential Equations].

Lyapunov spectral intervals: theory and computation [Appeared in SIAM J. Numerical Analysis]

Lyapunov and other spectra: a survey [Appeared in SIAM book on "Preservation of stability under discretization", D. Estep and S. Tavener Eds.].

Continuation of eigendecompositions [Appeared in FGCS: Future Generation Computer Systems -- Computational Science].

Point-to-Periodic and Periodic-to-Periodic Connections [April 19, 2004. Appeared in BIT].

Lyapunov and Sacker-Sell Spectral Intervals [Appeared in J.Dynamics and Differential Equations].

Continuation of Singular Value Decompositions [January 28, 2005. Appeared in Med. J. Mathematics].

On the error in computing Lyapunov exponents by QR methods [June 14, 2005. Appeared in Numerische Mathematik].

Smooth SVD on symplectic group and Lyapunov exponents approximation [July 19, 2005. Appeared in Calcolo].

The singular value decomposition to approximate spectra of dynamical systems. Theoretical aspects [August 7, 2006. Appeared in Journal of Differential Equations].

SVD algorithms to approximate spectra of dynamical systems. [August 24, 2007. Mathematics and Computers in Simulations (in press, 2008)].

A geometrical method for the approximation of invariant tori. [Appeared in Journal of Computational and Applied Mathematics (2008).]

Path following by SVD [December 16, 2005. Appeared in Lecture Notes in Computer Science--Springer].

Perturbation theory for approximation of Lyapunov exponents by QR methods [March 17, 2006. Appeared in J.Dynamics and Differential Equations].

Smoothness of Hessenberg and bidiagonal forms [Appeared in Med. J. Mathematics (2008)].

On the error in QR integration [August 9, 2007. To appear in SIAM J. Numerical Analysis].

Two parameter SVD: Coalescing singular values and periodicity. [August 13, 2008. To appear in SIAM J. Matrix Analysis & Applications.]

Singular values of two-parameter matrices: An algorithm to accurately find their intersections. [Mathematics and Computers in Simulations (2008, in press)].

Sliding motion in Filippov differential systems: Theoretical results and a computational approach. [January 20, 2009. To appear in SIAM J. Numerical Analysis.]

Locating coalescing singular values of large two parameter matrices. [January 19, 2009. To appear in Mathematics and Computers in Similations.]

Fundamental matrix solutions of piecewise smooth differential systems. [May 13, 2009. To appear in Mathematics and Computers in Simulations.]

Exponential Dichotomy on the real line: SVD and QR methods. [July 7, 2009. To appear in Journal of Differential Equations.]