A Low Processing Cost Adaptive Algorithm Identifying Nonlinear Unknown System with Piecewise Linear Curve

Though, in most practical applications, the length of the adaptive filter is less than that of the unknown system impulse response, analysis of adaptive filtering algorithms almost always assumed a sufficient length adaptive filter whose length is equal to that of unknown system. Theoretical results on the sufficient length adaptive algorithm do not necessarily apply to the realistic insufficient length case and, therefore, it becomes extremely desirable for practical purposes that we quantify the statistical behavior of the insufficient length adaptive algorithm. In this paper, we analyze the popular Transform Domain LMS (TDLMS) algorithm with insufficient length adaptive filter for Gaussian input data and using the common independence assumption. Analysis yields exact theoretical expressions that describe the mean and mean-square convergence of the algorithm, which lead to a better understanding to the performance properties of the insufficient length TDLMS adaptive algorithm. Simulation experiments illustrate the accuracy of the theoretical results in predicting the convergence behavior of the algorithm.

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A Space-Time Adaptive Algorithm to Illustrate the Lack of Collision of a Rigid Disk Falling in an Incompressible Fluid

Computational Methods in Applied Mathematics ◽

10.1515/cmam-2020-0046 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Samuel Dubuis ◽

Marco Picasso ◽

Peter Wittwer

Keyword(s):

Adaptive Algorithm ◽

Piecewise Linear ◽

A Posteriori Error Estimates ◽

Time Discretization ◽

Posteriori Error ◽

Space Time ◽

Rigid Disk ◽

Incompressible Viscous Flow ◽

Space Discretization ◽

Solid Bodies

AbstractA space-time adaptive algorithm to solve the motion of a rigid disk in an incompressible Newtonian fluid is presented, which allows collision or quasi-collision processes to be computed with high accuracy. In particular, we recover the theoretical result proven in [M. Hillairet, Lack of collision between solid bodies in a 2D incompressible viscous flow, Comm. Partial Differential Equations 32 2007, 7–9, 1345–1371], that the disk will never touch the boundary of the domain in finite time. Anisotropic, continuous piecewise linear finite elements are used for the space discretization, the Euler scheme for the time discretization. The adaptive criteria are based on a posteriori error estimates for simpler problems.

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Adaptive Algorithm for Three-Dimensional Mesh Generation Based on Constrained Delaunay

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001418550170 ◽

2018 ◽

Vol 32 (09) ◽

pp. 1855017 ◽

Cited By ~ 2

Author(s):

Longquan Zhou ◽

Xinming Lu ◽

Hongjuan Wang ◽

Wei Zhang ◽

Yanjun Peng ◽

...

Keyword(s):

Mesh Generation ◽

Adaptive Algorithm ◽

Piecewise Linear ◽

Three Dimensional ◽

Adaptive Mesh ◽

Adaptive Mesh Generation ◽

Size Function ◽

Wide Range ◽

Experimental Comparisons

Mesh generation is a key step for many areas. Here, an adaptive mesh generation algorithm for piecewise linear domains based on constrained Delaunay is proposed. We focus on improving the quality of the meshes generated and make them conforming to an isotropic size function which is specified by the user. The preliminary mesh with boundaries conforming is generated first. We try to add points to split the mesh either bad shape or not conforming to the size function. The new point can be added to the domain only if it is not close to the existing point in the domain. Finally, local meshes are reconstructed to make all meshes comply with the constrained Delaunay. Experimental comparisons show that the new algorithm is advantageous in generating adaptive mesh. The presented method can be used in a wide range of areas such as computer vision, finite element method and many other areas.

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An adaptive algorithm for the Stokes problem using continuous, piecewise linear stabilized finite elements and meshes with high aspect ratio

Applied Numerical Mathematics ◽

10.1016/j.apnum.2004.09.014 ◽

2005 ◽

Vol 54 (3-4) ◽

pp. 470-490 ◽

Cited By ~ 6

Author(s):

M. Picasso

Keyword(s):

Finite Elements ◽

Aspect Ratio ◽

High Aspect Ratio ◽

Adaptive Algorithm ◽

Stokes Problem ◽

Piecewise Linear ◽

Stabilized Finite Elements

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Processing cost and its consequences

Behavioral and Brain Sciences ◽

10.1017/s0140525x15000916 ◽

2016 ◽

Vol 39 ◽

Author(s):

William O'Grady

Keyword(s):

Word Order ◽

Proximity Effects ◽

Processing Cost

AbstractI focus on two challenges that processing-based theories of language must confront: the need to explain why language has the particular properties that it does, and the need to explain why processing pressures are manifested in the particular way that they are. I discuss these matters with reference to two illustrative phenomena: proximity effects in word order and a constraint on contraction.

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