A geometric algorithm for winding number computation with complexity analysis

Zapata, J.; Martín, Juan Carlos Díaz

doi:10.1016/j.jco.2012.02.001

Cited by 12 publications

(3 citation statements)

References 17 publications

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“…This equation is nothing but the discrete dispersion relation of the finite difference scheme (13), with frequency parameter κ in space and z in time. It is formally obtained by looking for solutions to the interior equation ( 13) having the form U n j = z n κ j .…”

Section: 1mentioning

confidence: 99%

“…Instead of computing (κ j (z)) j for each z on the unit circle independently, one may use the continuity of (κ j (z)) j with respect to z in order to describe the movement of the roots (κ j (z)) j for z ∈ S. After drawing the Kreiss-Lopatinskii curve, the winding number has to be computed in order to use Method 15. To do so, we use the geometric algorithm proposed by García Zapata and Díaz Martín in [13] and [14]. 4.3.…”

Section: Where Z Livesmentioning

confidence: 99%

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Stability of finite difference schemes for the hyperbolic initial boundary value problem by winding number computations

Boutin¹,

Barbenchon²,

Seguin³

2023

Preprint

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In this paper, we present a numerical strategy to check the strong stability (or GKSstability) of one-step explicit finite difference schemes for the one-dimensional advection equation with an inflow boundary condition. The strong stability is studied using the Kreiss-Lopatinskii theory. We introduce a new tool, the intrinsic Kreiss-Lopatinskii determinant, which possesses the same regularity as the vector bundle of discrete stable solutions. By applying standard results of complex analysis to this determinant, we are able to relate the strong stability of numerical schemes to the computation of a winding number, which is robust and cheap. The study is illustrated with the O3 scheme and the fifth-order Lax-Wendroff (LW5) scheme together with a reconstruction procedure at the boundary.

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Section: 1mentioning

confidence: 99%

Section: Where Z Livesmentioning

confidence: 99%

Stability of finite difference schemes for the hyperbolic initial boundary value problem by winding number computations

Boutin¹,

Barbenchon²,

Seguin³

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Turning Angle Method [27]: This method follows the counterclockwise order of vertices along the boundary of the zone polygon. It entails calculating whether positive or negative angles are formed by connecting each vertex with the reference point.…”

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confidence: 99%

Statistical Modeling of Water Shortage in Water Distribution Systems in Guangzhou

Cheng,

Luo,

Long

et al. 2023

Water

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In this study, data on water shortage events were collected from customer service systems. An analysis was conducted to establish the relationship between customers’ complaints and the water pressure flow conditions. A mathematical model was developed to estimate the probability of water shortage events based on water head. The Sigmoid function is commonly used as an activation function in neural networks. The function of the model is the same as the Sigmoid function, and its critical parameters correspond to the service head requirements of water facilities. By considering the interaction between human emotions and artificial systems, this study provides novel insights into improving the operational control and construction of water distribution systems.

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Counting Roots of a Polynomial in a Convex Compact Region by Means of Winding Number Calculation via Sampling

Zaderman

Zhao

2019

Computer Algebra in Scientific Computing

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In this paper, we propose a novel efficient algorithm for calculating winding numbers, aiming at counting the number of roots of a given polynomial in a convex region on the complex plane. This algorithm can be used for counting and exclusion tests in a subdivision algorithms for polynomial root-finding, and would be especially useful in application scenarios where high-precision polynomial coefficients are hard to obtain but we succeed with counting already by using polynomial evaluation with lower precision. We provide the pseudo code of the algorithm, proof of its correctness as well as estimation of its complexity.

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A geometric algorithm for winding number computation with complexity analysis

Cited by 12 publications

References 17 publications

Stability of finite difference schemes for the hyperbolic initial boundary value problem by winding number computations

Stability of finite difference schemes for the hyperbolic initial boundary value problem by winding number computations

Statistical Modeling of Water Shortage in Water Distribution Systems in Guangzhou

Counting Roots of a Polynomial in a Convex Compact Region by Means of Winding Number Calculation via Sampling

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