Results 31 to 40 of about 2,905,950 (213)
Symplectic integration without roundoff error [PDF]
, 2006 Most numerical integration algorithms are not designed specifically for Hamiltonian systems and do not respect their characteristic properties, which include the preservation of phase space volume with time. This can lead to spurious damping or excitation.
openaire +2 more sources
Roundoff error analysis of the CholeskyQR2 algorithm in an oblique inner product
JSIAM Letters, 2016 The Cholesky QR algorithm is an ideal QR decomposition algorithm for high performance computing, but known to be unstable. We present error analysis of the Cholesky QR algorithm in an oblique inner product defined by a positive definite matrix, and show ...
Yusaku Yamamoto +3 more
semanticscholar +1 more source
On numerical stability of continued fractions
Математичні СтудіїThe paper considers the numerical stability of the backward recurrence algorithm (BR-algorithm) for computing approximants of the continued fraction with complex elements.
V. Hladun +3 more
doaj +1 more source
Numerical Stability of Lanczos Methods [PDF]
, 1999 The Lanczos algorithm for matrix tridiagonalisation suffers from strong numerical instability in finite precision arithmetic when applied to evaluate matrix eigenvalues. The mechanism by which this instability arises is well documented in the literature.
Alan Irving +8 more
core +2 more sources
Journal of Time Series Analysis, Volume 47, Issue 2, Page 279-303, March 2026.This article reviews and compares popular methods, some old and some recent, that produce time series having Poisson marginal distributions. The article begins by narrating ways where time series with Poisson marginal distributions can be produced.
Jiajie Kong, Robert Lund
wiley +1 more source
Improved Accuracy and Parallelism for MRRR-based Eigensolvers -- A Mixed Precision Approach [PDF]
, 2013 The real symmetric tridiagonal eigenproblem is of outstanding importance in numerical computations; it arises frequently as part of eigensolvers for standard and generalized dense Hermitian eigenproblems that are based on a reduction to tridiagonal form.
Bientinesi, Paolo +2 more
core +2 more sources
Geophysical Research Letters, Volume 53, Issue 2, 28 January 2026.Abstract Machine learning (ML) weather models like GraphCast and NeuralGCM show forecasting promise but face fundamental limitations for data assimilation (DA) integration. This study reveals critical problems in error covariance representation and adjoint sensitivity patterns challenging their operational viability.
Xiaoxu Tian +2 more
wiley +1 more source
Roundoff Error Analysis of the Fast Fourier Transform [PDF]
Mathematics of Computation, 1971 This paper presents an analysis of roundoff errors occurring in the floating-point computation of the fast Fourier transform. Upper bounds are derived for the ratios of the root-mean-square (RMS) and maximum roundoff errors in the output data to the RMS value of the output data for both single and multidimensional transformations.
openaire +2 more sources
How Accurate is Richardson's Error Estimate?
Concurrency and Computation: Practice and Experience, Volume 37, Issue 27-28, 25 December 2025.ABSTRACT We consider the fundamental problem of estimating the difference between the exact value T$$ T $$ and approximations Ah$$ {A}_h $$ that depend on a single real parameter h$$ h $$. It is well‐known that if the error Eh=T−Ah$$ {E}_h=T-{A}_h $$ satisfies an asymptotic expansion, then we can use Richardson extrapolation to approximate Eh$$ {E}_h $$
Carl Christian Kjelgaard Mikkelsen +1 more
wiley +1 more source
Математичні СтудіїIn this paper, we consider some numerical aspects of branched continued fractions as special families of functions to represent and expand analytical functions of several complex variables, including generalizations of hypergeometric functions.
R. Dmytryshyn +3 more
doaj +1 more source