# Numerical stability

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In the mathematical subfield of numerical analysis, numerical stability is a desirable property of numerical algorithms. (Wikipedia.org)

# 4,610 resources related to Numerical stability

### Conferences related to Numerical stability

2020 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting

The joint meeting is intended to provide an international forum for the exchange of information on state of the art research in the area of antennas and propagation, electromagnetic engineering and radio science

2020 American Control Conference (ACC)

The ACC is the annual conference of the American Automatic Control Council (AACC, the U.S. national member organization of the International Federation for Automatic Control (IFAC)). The ACC is internationally recognized as a premier scientific and engineering conference dedicated to the advancement of control theory and practice. The ACC brings together an international community of researchers and practitioners to discuss the latest findings in automatic control. The 2020 ACC technical program will

2020 IEEE International Conference on Robotics and Automation (ICRA)

The International Conference on Robotics and Automation (ICRA) is the IEEE Robotics and Automation Society’s biggest conference and one of the leading international forums for robotics researchers to present their work.

2020 IEEE International Conference on Systems, Man, and Cybernetics (SMC)

The 2020 IEEE International Conference on Systems, Man, and Cybernetics (SMC 2020) will be held in Metro Toronto Convention Centre (MTCC), Toronto, Ontario, Canada. SMC 2020 is the flagship conference of the IEEE Systems, Man, and Cybernetics Society. It provides an international forum for researchers and practitioners to report most recent innovations and developments, summarize state-of-the-art, and exchange ideas and advances in all aspects of systems science and engineering, human machine systems, and cybernetics. Advances in these fields have increasing importance in the creation of intelligent environments involving technologies interacting with humans to provide an enriching experience and thereby improve quality of life. Papers related to the conference theme are solicited, including theories, methodologies, and emerging applications. Contributions to theory and practice, including but not limited to the following technical areas, are invited.

2020 IEEE Power & Energy Society General Meeting (PESGM)

The Annual IEEE PES General Meeting will bring together over 2900 attendees for technical sessions, administrative sessions, super sessions, poster sessions, student programs, awards ceremonies, committee meetings, tutorials and more

### Periodicals related to Numerical stability

Experimental and theoretical advances in antennas including design and development, and in the propagation of electromagnetic waves including scattering, diffraction and interaction with continuous media; and applications pertinent to antennas and propagation, such as remote sensing, applied optics, and millimeter and submillimeter wave techniques.

Contains articles on the applications and other relevant technology. Electronic applications include analog and digital circuits employing thin films and active devices such as Josephson junctions. Power applications include magnet design as well asmotors, generators, and power transmission

The theory, design and application of Control Systems. It shall encompass components, and the integration of these components, as are necessary for the construction of such systems. The word `systems' as used herein shall be interpreted to include physical, biological, organizational and other entities and combinations thereof, which can be represented through a mathematical symbolism. The Field of Interest: shall ...

Part I will now contain regular papers focusing on all matters related to fundamental theory, applications, analog and digital signal processing. Part II will report on the latest significant results across all of these topic areas.

Part I will now contain regular papers focusing on all matters related to fundamental theory, applications, analog and digital signal processing. Part II will report on the latest significant results across all of these topic areas.

### Xplore Articles related to Numerical stability

Tsinghua Science and Technology, 2007

This paper presents an algorithm for identifying desirable multiple targets in an intracellular regulation network. The algorithm is based on constrained state feedback and Monte-Carlo simulations. The computational complexity of the algorithm increases linearly with increasing the number of species in a gene regulation system. An estimate is derived for the confidence level of the predicted minimum required perturbation strength ...

Tsinghua Science and Technology, 2006

The objective of this paper is to analyze the stability of equilibrium manifolds for a ratio-dependent two-predators one-prey model. Some model results are presented first with the bifurcation without parameters method, and then the method was used to study bifurcation along the equilibrium manifold for the model. The model does not lose stability even when some equilibria are locally unstable ...

NDES 2012; Nonlinear Dynamics of Electronic Systems, 2012

Stability of a power grid’s synchronous operating mode is crucial to its reliable function. We quantify the stability of this operating mode in different humble power grid layouts that we numerically simulate employing a widely used electro-mechanical model. The method with which we quantify stability delivers a single number, called basin stability, for each node in a grid. A node ...

An efficient x-recursive numerical scheme is presented to compute Legendre polynomials P<inf>n</inf>(x) and their derivatives P'<inf>n</inf>(x) on the interval (0, 1) for a fixed-order <tex>$n\in\mathbb{N}$</tex>. The numerical properties are discussed and, as an example of use in computational electromagnetics, the method is applied to improve a recently proposed spherical-multipole based time domain near-to-far-field transformation algorithm.

Tsinghua Science and Technology, 2004

The Taylor series numerical method (TSNM) is a time integration method for solving problems in structural dynamics. In this paper, a detailed analysis of the stability behavior and accuracy characteristics of this method is given. It is proven by a spectral decomposition method that TSNM is conditionally stable and belongs to the category of explicit time integration methods. By a ...

### Educational Resources on Numerical stability

#### IEEE-USA E-Books

• This paper presents an algorithm for identifying desirable multiple targets in an intracellular regulation network. The algorithm is based on constrained state feedback and Monte-Carlo simulations. The computational complexity of the algorithm increases linearly with increasing the number of species in a gene regulation system. An estimate is derived for the confidence level of the predicted minimum required perturbation strength when targets are prescribed a priori. The algorithm has been used to analyze the cell cycle of Xenopus frog eggs. The results agree well with available results for single target perturbations, and multitarget interference is usually not equal to the summation of the single-target interferences.

• The objective of this paper is to analyze the stability of equilibrium manifolds for a ratio-dependent two-predators one-prey model. Some model results are presented first with the bifurcation without parameters method, and then the method was used to study bifurcation along the equilibrium manifold for the model. The model does not lose stability even when some equilibria are locally unstable because the equilibrium manifold is stable when treated as a whole. The ecological implications of the results are discussed.

• Stability of a power grid’s synchronous operating mode is crucial to its reliable function. We quantify the stability of this operating mode in different humble power grid layouts that we numerically simulate employing a widely used electro-mechanical model. The method with which we quantify stability delivers a single number, called basin stability, for each node in a grid. A node with a poor basin stability is a weak point, as a rather small perturbation to this node would suffice to destroy the synchrony of the whole system and make it collapse. Using tools from the theory of complex networks, we statistically evaluate an ensemble of grids to identify topological classes of nodes whose members typically have the same (poor or large) value of basin stability.

• An efficient x-recursive numerical scheme is presented to compute Legendre polynomials P<inf>n</inf>(x) and their derivatives P'<inf>n</inf>(x) on the interval (0, 1) for a fixed-order <tex>$n\in\mathbb{N}$</tex>. The numerical properties are discussed and, as an example of use in computational electromagnetics, the method is applied to improve a recently proposed spherical-multipole based time domain near-to-far-field transformation algorithm.

• The Taylor series numerical method (TSNM) is a time integration method for solving problems in structural dynamics. In this paper, a detailed analysis of the stability behavior and accuracy characteristics of this method is given. It is proven by a spectral decomposition method that TSNM is conditionally stable and belongs to the category of explicit time integration methods. By a similar analysis, the characteristic indicators of time integration methods, the percentage period elongation and the amplitude decay of TSNM, are derived in a closed form. The analysis plays an important role in implementing a procedure for automatic searching and finding convergence radii of TSNM. Finally, a linear single degree of freedom undamped system is analyzed to test the properties of the method.

• A novel Fast RLS Algorithm based on the Givens Rotation and developed from an UDU<sup>T</sup> square-root factorization of autocorrelation matrix is discussed. The algorithm presents excellent numerical properties and requires 14N multiplications and 6N divisions per sampling interval, where N is the linear filter order.

• Based on the second-order compact upwind scheme, a group explicit method for solving the two-dimensional time-independent convection-dominated diffusion problem is developed. The stability of the group explicit method is proven strictly. The method has second-order accuracy and good stability. This explicit scheme can be used to solve all Reynolds number convection-dominated diffusion problems. A numerical test using a parallel computer shows high efficiency. The numerical results conform closely to the analytic solution.

• The present paper investigates a stabilization of unstable steady states in a pair of limit-cycle oscillators coupled by a partial time-varying delay connection. This connection has two connection delays: time-varying delay and time-invariant delay. A linear stability analysis allows us to obtain the stability regions in a connection parameter space. It is shown that the partial time-varying delay connection enlarges the stability region as compared with the conventional time-invariant delay connection. The analytical results are confirmed by numerical simulations.

• Considering a linear system of delay integro-differential equations with a constant delay whose zero solution is asympototically stable, this paper discusses the stability of numerical methods for the system. The adaptation of Runge-Kutta methods with a Lagrange interpolation procedure was focused on inheriting the asymptotic stability of underlying linear systems. The results show that an A-stable RungeKutta method preserves the asympototic stability of underlying linear systems whenever an unconstrained grid is used.

• This work reviews the topic of two-port unconditional stability (US) and fixes some misconceptions still common among high-frequency designers, notwithstanding the broad, relevant literature. Ohtomo's test for network stability is then presented in a synthetic form and linked to US conditions. Finally, this approach is extended to N-port networks to obtain two sets of US conditions, which are intuitive generalizations of results well known in the two-port case. These conditions represent a necessary complement to the few works which have discussed three-port US up to now, since they only focus on the geometrical part of the problem, omitting to explicitly take care of Rollett's proviso and its implications on US.