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Mathematics: Recent submissions
Now showing items 201-220 of 462
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A new scaling for Newton's iteration for the polar decomposition and its backward stability
(Society for Industrial and Applied Mathematics, 2008-04-27)We propose a scaling scheme for Newton's iteration for calculating the polar decomposition. The scaling factors are generated by a simple scalar iteration in which the initial value depends only on estimates of the extreme ... -
Euclidean proofs of projective geometry theorems /
(University of Kansas, 1922.) -
A Shadowing Lemma Approach to Global Error Analysis for Initial Value ODEs
(Society for Industrial and Applied Mathematics, 1994-04-05)The authors show that for dynamical systems that possess a type of piecewise hyperbolicity in which there is no decrease in the number of stable modes, the global error in a numerical approximation may be obtained as a ... -
Unitary Integrators and Applications to Continuous Orthonormalization Techniques
(Society for Industrial and Applied Mathematics, 1994-09-05)In this paper the issue of integrating matrix differential systems whose solutions are unitary matrices is addressed. Such systems have skew-Hermitian coefficient matrices in the linear case and a related structure in the ... -
Numerical Shadowing Near Hyperbolic Trajectories
(Society for Industrial and Applied Mathematics, 1995-04-05)Shadowing is a means of characterizing global errors in the numerical solution of initial value ordinary differential equations by allowing for a small perturbation in the initial condition. The method presented in this ... -
On the Compuation of Lyapunov Exponents for Continuous Dynamical Systems
(Society for Industrial and Applied Mathematics, 1997-02-05)In this paper, we consider discrete and continuous QR algorithms for computing all of the Lyapunov exponents of a regular dynamical system. We begin by reviewing theoretical results for regular systems and present general ... -
Diffusion Induced Chaos in a Closed Loop Thermosyphon
(Society for Industrial and Applied Mathematics, 1998-08-05)The dynamics of a closed loop thermosyphon are considered. The model assumes a prescribed heat flux along the loop wall and the contribution of axial diffusion. The well-posedness of the model which consists of a coupled ... -
Traveling Wave Solutions for Systems of ODEs on a Two-Dimensional Spatial Lattice
(Society for Industrial and Applied Mathematics, 1999-03-05)We consider infinite systems of ODEs on the two-dimensional integer lattice, given by a bistable scalar ODE at each point, with a nearest neighbor coupling between lattice points. For a class of ideal nonlinearities, we ... -
Numerical Shadowing Using Componentwise Bounds and a Sharper Fixed Point Result
(Society for Industrial and Applied Mathematics, 2001-03-05)Shadowing provides a means of obtaining global error bounds for approximate solutions of nonlinear differential equations with interesting dynamics, in particular, for initial value problems with positive Lyapunov exponents. ... -
Traveling Waves Solutions for Bistable Differential-Difference Equations with Periodic Diffusion
(Society for Industrial and Applied Mathematics, 2001-10-05)We consider traveling wave solutions to spatially discrete reaction-diffusion equations with nonlocal variable diffusion and bistable nonlinearities. To find the traveling wave solutions we introduce an ansatz in which the ... -
Lyapunov Spectral Intervals: Theory and Computation
(Society for Industrial and Applied Mathematics, 2002-05-05)Different definitions of spectra have been proposed over the years to characterize the asymptotic behavior of nonautonomous linear systems. Here, we consider the spectrum based on exponential dichotomy of Sacker and Sell ... -
Spatially Discrete FitzHugh-Nagumo Equations
(Society for Industrial and Applied Mathematics, 2005-04-05)We consider pulse and front solutions to a spatially discrete FitzHugh--Nagumo equation that contains terms to represent both depolarization and hyperpolarization of the nerve axon. We demonstrate a technique for deriving ... -
Computation of Mixed Type Functional Differential Boundary Value Problems
(Society for Industrial and Applied Mathematics, 2005-09-05)We study boundary value differential-difference equations where the difference terms may contain both advances and delays. Special attention is paid to connecting orbits, in particular to the modeling of the tails after ... -
Traveling Wave Solutions to a Coupled System of Spatially Discrete Nagumo Equations
(Society for Industrial and Applied Mathematics, 2006-07-31)We consider a coupled system of discrete Nagumo equations and derive traveling wave solutions to this system using McKean's caricature of the cubic. A certain form of this system is used to model ephaptic coupling between ... -
On the Error in QR Integration
(Society for Industrial and Applied Mathematics, 2008-03-07)An important change of variables for a linear time varying system $\dot x=A(t)x, t\ge 0$, is that induced by the QR-factorization of the underlying fundamental matrix solution: $X=QR$, with Q orthogonal and R upper triangular ... -
On the Error in the Product QR Decomposition
(Society for Industrial and Applied Mathematics, 2010-03-17)We develop both a normwise and a componentwise error analysis for the QR factorization of long products of invertible matrices. We obtain global error bounds for both the orthogonal and upper triangular factors that depend ... -
Front Solutions for Bistable Differential-Difference Equations with Inhomogeneous Diffusion
(Society for Industrial and Applied Mathematics, 2011-08-09)We consider a bistable differential-difference equation with inhomogeneous diffusion. Employing a piecewise linear nonlinearity, often referred to as McKean's caricature of the cubic, we construct front solutions which ... -
Traveling Wavefronts in an Antidiffusion Lattice Nagumo Model
(Society for Industrial and Applied Mathematics, 2011-06-06)We consider a system of lattice Nagumo equations with cubic nonlinearity, but with a negative discrete diffusion coefficient. We are interested in the existence, uniqueness, stability, and nonexistence of the traveling ... -
Singular function mortar finite element methods
(De Gruyter Open, 2003-01-05)We consider the Poisson equation with Dirichlet boundary conditions on a polygonal domain with one reentrant corner. We introduce new nonconforming finite element discretizations based on mortar techniques and singular ... -
Three-level BDDC in three dimensions
(Society for Industrial and Applied Mathematics, 2007-10-05)Balancing domain decomposition by constraints (BDDC) methods are nonoverlapping iterative substructuring domain decomposition methods for the solution of large sparse linear algebraic systems arising from the discretization ...
