Results 221 to 230 of about 191,474 (264)

Numerical stabilization of polynomial and matrix

IMA Journal of Mathematical Control and Information, 2006
In this paper, the conception of numerical stabilization, which is related to mantissa digits of computer and dimensions of system, is described; and several strategies for the numerical stabilization of polynomial and matrix are presented.
J. D. Han, Z. Jiang, Yiyong Nie
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On the numerical stability of algorithmic differentiation

Computing, 2011
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Andreas Griewank, Kshitij Kulshreshtha, Andrea Walther   +2 more
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Numerical Stability of the Parallel Jacobi Method

SIAM Journal on Matrix Analysis and Applications, 2005
The authors analyse the numerical stability of the parallel Jacobi method for computing the singular values and singular subspaces of an invertible upper triangular matrix obtained from QR decomposition with column pivoting. They show that in this case the parallel Jacobi method works with full machine accuracy, thus the computational errors are ...
Tristan Londré, Noah H. Rhee
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Numerical Stabilization of Orbital Motion

Celestial Mechanics and Dynamical Astronomy, 2003
Mainly, the author focuses on Baumgarte's method and its applications in satellite, asteroid, stellar and planetary problems. In the paper arguments are given for the use of energy relations for stabilization in the elliptical two-body problem. Stabilizing properties of Baumgarte's equations and others are discussed.
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Numerical stability of GMRES

BIT Numerical Mathematics, 1995
The generalized minimal residual (GMRES) method is one of the most popular methods for solving systems of linear equations with nonsymmetric coefficient matrices. The authors study the numerical stability of GMRES when the computation of approximations is based on constructing an orthonormal basis of Krylov subspaces (Arnoldi basis) and after that the ...
Drkošová, J., Greenbaum, A., Rozložník, M., Strakoš, Z.   +3 more
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Stability of the Numerical Method

2016
Stability in numerical analysis means that the approximate solutions admit the same bounds as indicated by the a priori estimates for the original problem. The fact that the numerical solutions satisfy the energy inequality ( 7.28) plays a crucial role.
Eduard Feireisl, Trygve G. Karper, Milan Pokorný   +2 more
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Stability of a Numerical Solution of Differential Equations

Journal of the ACM, 1959
In 1926 Milne [1] published a numerical method for the solution of ordinary differential equations. This method turns out to be unstable, as shown by Muhin [2], Hildebrand [3], Liniger [4], and others. Instability was not too serious in the day of desk calculators but is fatal in the modern era of high speed computers.
W. E. Milne, R. R. Reynolds
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Numerical Stability Properties

2008
Designers of algorithms must not only solve the problem of interest, but do so using methods which are robust under perturbations in the data as well as the intermediate parameters of the method. More generally, it is often the case that the actual problem of interest is too complicated to solve directly; simplifying assumptions are necessary.
Phillip Regalia, Richard Le Borne
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The Numerical Stability of Observability

1990
The problem of recovering the initial data of the system x = Ax, y = cx, x(0) = x 0 from the data (y(t 1), y(t 2),…, y(t n )) is considered. It is shown that in general the problem is numerically ill-conditioned for any choice of sampling times t 1 < t 2 < … < t n . In some cases the lower bound for the condition number is obtained.
Clyde Martin, Ilias Iakovidis
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On numerical stability

1984
Since desk-calculators have been replaced by personal computers, terminals or at least programmable pocket-calculators, it is not possible to follow the execution of an algorithm by the computer step by step. One only sees the result and to judge the acceptability of this result other expedients are necessary.
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