On the Error in QR Integration

DOI10.1137/06067818XzbMath1170.65068OpenAlexW2134009775MaRDI QIDQ3631911

Luca Dieci, Erik S. Van Vleck

Publication date: 22 June 2009

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/06067818x

zbMATH Keywords

Lyapunov exponentserror boundsbackward error analysisforward error analysisintegral separationQR methodsQR-factorizationorthogonal integration

Mathematics Subject Classification ID

Factorization of matrices (15A23) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70)

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Evans function computation for the stability of travelling waves ⋮ Root Following in Evans Function Computation ⋮ Projected Shadowing-Based Data Assimilation ⋮ Exponential dichotomy for asymptotically hyperbolic two-dimensional linear systems ⋮ On the error in approximating stability spectra for discrete dynamical systems ⋮ Approximating Lyapunov exponents and Sacker-Sell spectrum for retarded functional differential equations ⋮ Detecting exponential dichotomy on the real line: SVD and QR algorithms ⋮ \(QR\) methods and error analysis for computing Lyapunov and Sacker--Sell spectral intervals for linear differential-algebraic equations ⋮ A simple technique for calculation of numerical integration errors for physically meaningful functions ⋮ A step-size selection strategy for explicit Runge-Kutta methods based on Lyapunov exponent theory ⋮ Fluid deformation in random steady three-dimensional flow

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