Results 11 to 20 of about 3,221,012 (201)

Certified Roundoff Error Bounds Using Semidefinite Programming. [PDF]

ACM Transactions on Mathematical Software, 2015
Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance for FPGAs or custom ...
Constantinides, GA, Donaldson, AF, Magron, V   +2 more
core   +9 more sources

General moments of roundoff error [PDF]

Communications in Statistics - Simulation and Computation, 2019
Li and Nadarajah [Signal Processing 127 (2016) 185–190] derived expressions for mean and variance of roundoff error for any continuous random variable. Here, we derive expressions for general moments of the roundoff error, allowing one to study other aspects of roundoff error than just mean and variance.
Martin Wiegand, Saralees Nadarajah
openaire   +3 more sources

Roundoff Error Analysis of an Algorithm Based on Householder Bidiagonalization for Total Least Squares Problems

Mathematics, 2021
For large-scale problems, how to establish an algorithm with high accuracy and stability is particularly important. In this paper, the Householder bidiagonalization total least squares (HBITLS) algorithm and nonlinear iterative partial least squares for ...
Zhanshan Yang, Xilan Liu
doaj   +3 more sources

Certified Roundoff Error Bounds using Bernstein Expansions and Sparse Krivine-Stengle Representations [PDF]

IEEE Symposium on Computer Arithmetic, 2017
Floating point error is an inevitable drawback of embedded systems implementation. Computing rigorous upper bounds of roundoff errors is absolutely necessary to the validation of critical software.
Dang, Thao, Magron, Victor, Rocca, Alexandre   +2 more
core   +8 more sources

Stochastic Estimation of MIMO Detection Error Caused by Low-Bitwidth QR Decomposition

IEEE Open Journal of the Communications Society
In this paper, we propose a new approach to justify a roundoff error impact on the accuracy of the linear least squares (LS) solution using QR decomposition.
Alexander Osinsky, Roman Bychkov, Mikhail Kirichenko, Vladimir Lyashev, Andrey Ivanov   +4 more
doaj   +2 more sources

Rigorous Roundoff Error Analysis of Probabilistic Floating-Point Computations [PDF]

International Conference on Computer Aided Verification, 2021
We present a detailed study of roundoff errors in probabilistic floating-point computations. We derive closed-form expressions for the distribution of roundoff errors associated with a random variable, and we prove that roundoff errors are generally ...
G. Constantinides, Fredrik Dahlqvist, Zvonimir Rakamarić, Rocco Salvia   +3 more
semanticscholar   +1 more source

QR Decomposition Based on Double-double Precision Gram-Schmidt Orthogonalization Method [PDF]

Jisuanji kexue, 2023
The Gram-Schmidt orthogonalization algorithm and its related modified algorithms often show numerical instability when computing ill-conditioned or large-scale matrices.To solve this problem,this paper explores the cumulative effect of round-off errors ...
JIN Jiexi, XIE Hehu, DU Peibing, QUAN Zhe, JIANG Hao
doaj   +1 more source

Mathematical modeling of parameter identification process of convection-diffusion transport models using the SVD-based Kalman filter [PDF]

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2021
The paper addresses a problem of mathematical modeling of the process of identifying the coefficients of a partial differential equation in convection-diffusion transport models based on the results of noisy measurements of the function values ...
Anastasia N. Kuvshinova, Andrey V. Tsyganov, Yulia V. Tsyganova   +2 more
doaj   +1 more source

Floating-Point Roundoff Error Analysis in Artificial Neural Networks

Proceedings of the 25th IMEKO TC4 International Symposium and 23rd International Workshop on ADC and DAC Modelling and Testing, 2022
– In this paper, roundoff errors in Artificial Neural Networks (ANNs) are analyzed on a model for Solid-State Power Amplifiers (SSPAs). Calculations are carried out on 32-bit Floating-Point (FP32) arithmetics, and results are verified using 64-bit floating ...
Hussein Al-Rikabi, B. Renczes
semanticscholar   +1 more source

Global error estimation of linear multistep methods through the Runge-Kutta methods [PDF]

Iranian Journal of Numerical Analysis and Optimization, 2016
In this paper, we study the global truncation error of the linear multistep methods (LMM) in terms of local truncation error of the corresponding Runge-Kutta schemes. The key idea is the representation of LMM with a corresponding Runge-Kutta method.
Javad Farzi
doaj   +1 more source