Results 11 to 20 of about 27,076 (290)

A New Approach to Probabilistic Rounding Error Analysis [PDF]

SIAM Journal on Scientific Computing, 2019
Summary: Traditional rounding error analysis in numerical linear algebra leads to backward error bounds involving the constant \(\gamma_n = nu/(1-nu)\), for a problem size \(n\) and unit roundoff \(u\). In light of large-scale and possibly low-precision computations, such bounds can struggle to provide any useful information.
Nicholas J. Higham, Théo Mary
exaly   +8 more sources

A Higher-Order Extended Cubature Kalman Filter Method Using the Statistical Characteristics of the Rounding Error of the System Model [PDF]

Mathematics
The cubature Kalman filter (CKF) cannot accurately estimate the nonlinear model, and these errors will have an impact on the accuracy. In order to improve the filtering performance of the CKF, this paper proposes a new CKF method to improve the ...
Haiyang Zhang, Chenglin Wen
doaj   +4 more sources

Probabilistic Rounding Error Analysis of Householder QR Factorization [PDF]

SIAM Journal on Matrix Analysis and Applications, 2023
The standard worst-case normwise backward error bound for Householder QR factorization of an m×n matrix is proportional to mnu, where u is the unit roundoff.
Nicholas Higham
exaly   +3 more sources

Probabilistic Error Analysis of Limited-Precision Stochastic Rounding [PDF]

SIAM Journal of Scientific Computing
Classical probabilistic rounding error analysis is particularly well suited to stochastic rounding (SR), and it yields strong results when dealing with floating-point algorithms that rely heavily on summation. For many numerical linear algebra algorithms,
Mantas Mikaitis, Silviu-Ioan Filip, Massimiliano Fasi   +2 more
exaly   +7 more sources

Methods of Combating the Accumulation of Rounding Error When Solving Problems of Trans-Computational Complexity [PDF]

Кібернетика та комп'ютерні технології
Introduction. The main attention is paid to the need to take into account estimates of rounding errors when solving problems of transcomputational complexity.
Valerii Zadiraka, Inna Shvidchenko
doaj   +2 more sources

Rounding-Error Analysis of Multigrid \({V}\)-Cycles

SIAM Journal on Scientific Computing
This paper provides a rounding-error analysis for two-grid methods that use one relaxation step both before and after coarsening. The analysis is based on floating point arithmetic and focuses on a two-grid scheme that is perturbed on the coarse grid to allow for an approximate coarse-grid solve.
Stephen F. McCormick, Rasmus Tamstorf
openaire   +4 more sources

Lossless audio coding using the IntMDCT and rounding error shaping [PDF]

, 2022
S.2201-2211In this paper, lossless audio coding using the integer modified discrete cosine transform (IntMDCT) is discussed. The IntMDCT is constructed as an integer approximation of the MDCT using the lifting scheme and is reversible. The rounding error
Schuller, G.D.T., Geiger, R., Yokotani, Y., Oraintara, S., Rao, K.R.   +4 more
core   +1 more source

Algorithm for Calculating Primary Spectral Density Estimates Using FFT and Analysis of its Accuracy

Кібернетика та комп'ютерні технології, 2022
Introduction. Fast algorithms for solving problems of spectral and correlation analysis of random processes began to appear mainly after 1965, when the algorithm of fast Fourier transform (FFT) entered computational practice.
Olena Kolomys, Liliya Luts
doaj   +1 more source

Statistical Analysis of Rounded Data: Measurement Errors vs Rounding Errors [PDF]

Journal of Mathematical Sciences, 2018
Consider the measurements in which the discretization step is constant and without loss of generality is equal to 1. The measured value \(X\) is rounded to the closest integer \(X^*\) according to the rule \(X^*=[X+0.5]\) where \([x]\) is the integer part of \(x\). Measurements of the quantity \(\mu\) are considered as i.i.d. random samples \(X_1,\dots,
Ushakov, Nikolai, Ushakov, Vladimir G.
openaire   +2 more sources

Computer Technology for Construction ε-Solution of the Problem

Кібернетика та комп'ютерні технології, 2023
Introduction. Issues of selection and construction of computing resources and methods of their effective use to calculate an approximate solution of the problem with the given accuracy in a limited processor time are considered.
Valerii Zadiraka, Inna Shvidchenko
doaj   +1 more source