An Error Functional Expansion for N-Dimensional Quadrature with an Integrand Function Singular at a Point

1976 ◽  
Vol 30 (133) ◽  
pp. 1 ◽  
Author(s):  
J. N. Lyness
Keyword(s):  
Functional Expansion ◽  
Error Functional ◽  
Integrand Function

Functional expansion pharyngoplasty: Technical update by unidirectional barbed sutures

2018 ◽  
Vol 43 (5) ◽  
pp. 1419-1421 ◽  
Author(s):  
G. Sorrenti ◽  
I. Pelligra ◽  
R. Albertini ◽  
G. Caccamo ◽  
O. Piccin
Keyword(s):  
Barbed Sutures ◽  
Functional Expansion

scholarly journals Functional Expansion of Sensorimotor Representation and Structural Reorganization of Callosal Connections in Lower Limb Amputees

2012 ◽  
Vol 32 (9) ◽  
pp. 3211-3220 ◽  
Author(s):  
E. L. Simoes ◽  
I. Bramati ◽  
E. Rodrigues ◽  
A. Franzoi ◽  
J. Moll ◽  
...  
Keyword(s):  
Lower Limb ◽  
Structural Reorganization ◽  
Callosal Connections ◽  
Functional Expansion ◽  
Lower Limb Amputees

Improving the Generalization Properties of Radial Basis Function Neural Networks

1991 ◽  
Vol 3 (4) ◽  
pp. 579-588 ◽  
Author(s):  
Chris Bishop
Keyword(s):  
Neural Networks ◽  
Radial Basis Function ◽  
Basis Function ◽  
Learning Algorithm ◽  
Error Functional ◽  
Radial Basis ◽  
The Error Functional ◽  
Network Mapping ◽  
Nonlinear Mappings

An important feature of radial basis function neural networks is the existence of a fast, linear learning algorithm in a network capable of representing complex nonlinear mappings. Satisfactory generalization in these networks requires that the network mapping be sufficiently smooth. We show that a modification to the error functional allows smoothing to be introduced explicitly without significantly affecting the speed of training. A simple example is used to demonstrate the resulting improvement in the generalization properties of the network.

scholarly journals Оптимальные формулы типа Эйлера-Маклорена для численного интегрирования в пространстве Соболева

2020 ◽  
pp. 75-101
Author(s):  
A.R. Hayotov ◽  
F.A. Nuraliev ◽  
R.I. Parovik ◽  
Kh.M. Shadimetov
Keyword(s):  
Discrete Analogue ◽  
Quadrature Formulas ◽  
Optimal Error ◽  
Integration Interval ◽  
Optimal Quadrature ◽  
Arbitrary Natural Number ◽  
Error Functional ◽  
Optimal Quadrature Formulas ◽  
The Space L2 ◽  
Derivatives Of

In the present paper the problem of construction of optimal quadrature formulas in the sense of Sard in the space  L2(m)(0,1) is considered. Here the quadrature sum consists of values of the integrand at nodes and values of the first and the third derivatives of the integrand at the end points of the integration interval. The coefficients of optimal quadrature formulas are found and the norm of the optimal error functional is calculated for arbitrary natural number N ≥ m-3 and for any m ≥ 4 using S. L. Sobolev method which is based on the discrete analogue of the differential operator d2m/dx2m. In particular, for m = 4 and m = 5 optimality of the classical Euler-Maclaurin quadrature formula is obtained. Starting from m=6 new optimal quadrature formulas are obtained. At the end of this work some numerical results are presented. В настоящей статье рассматривается задача построения оптимальных квадратурных формул в смысле Сарда в пространстве L2(m)(0,1). Здесь квадратурная сумма состоить из значений подынтегральной функции в узлах и значений первой и третьей производных подынтегральной функции на концах интервала интегрирования. Найдены коэффициенты оптимальных квадратурных формул и вычислена норма оптимального функционала погрешности для любого натурального числа N ≥ m-3 и для любого m ≥ 4, используя метод С. Л. Соболева который основывается на дискретный аналог дифференциального оператора d2m/dx2m. В частности, при m = 4 и m = 5 получен оптимальность классической формулы Эйлера-Маклорена. Начиная с m = 6 получены новые оптимальные квадратурные формулы. В конце работы приведаны некоторые численные результаты.

scholarly journals Minimization of an energy error functional to solve a Cauchy problem arising in plasma physics: the reconstruction of the magnetic flux in the vacuum surrounding the plasma in a Tokamak

2012 ◽  
Vol Volume 15, 2012 ◽  
Author(s):  
Blaise Faugeras ◽  
Amel Ben Abda ◽  
Jacques Blum ◽  
Cedric Boulbe
Keyword(s):  
Cauchy Problem ◽  
Magnetic Flux ◽  
Plasma Physics ◽  
Numerical Method ◽  
Numerical Experiments ◽  
Energy Error ◽  
Error Functional ◽  
International Audience

International audience A numerical method for the computation of the magnetic flux in the vacuum surrounding the plasma in a Tokamak is investigated. It is based on the formulation of a Cauchy problem which is solved through the minimization of an energy error functional. Several numerical experiments are conducted which show the efficiency of the method.

scholarly journals Comparison of two neural network approaches to modeling processes in a chemical reactor

2019 ◽  
Vol 23 (Suppl. 2) ◽  
pp. 583-589 ◽  
Author(s):  
Tatiana Shemyakina ◽  
Dmitriy Tarkhov ◽  
Alexander Vasilyev ◽  
Yulia Velichko
Keyword(s):  
Neural Network ◽  
Shooting Method ◽  
Chemical Reactor ◽  
Euler Method ◽  
Error Functional ◽  
Non Linear ◽  
Test Points ◽  
Linear Differential ◽  
Hidden Layer ◽  
Network Approaches

In this paper, we conduct the comparative analysis of two neural network approaches to the problem of constructing approximate neural network solutions of non-linear differential equations. The first approach is connected with building a neural network with one hidden layer by minimization of an error functional with regeneration of test points. The second approach is based on a new continuous analog of the shooting method. In the first step of the second method, we apply our modification of the corrected Euler method, and in the second and subsequent steps, we apply our modification of the St?rmer method. We have tested our methods on a boundary value problem for an ODE which describes the processes in the chemical reactor. These methods allowed us to obtain simple formulas for the approximate solution of the problem, but the problem is special because it is highly non-linear and also has ambiguous solutions and vanishing solutions if we change the parameter value.

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