Uniform convergence of derivatives of extended Lagrange interpolation

Criscuolo, G.; Mastroianni, G.

doi:10.1007/bf01385721

Cited by 12 publications

(4 citation statements)

References 20 publications

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“…In the context of our paper, this involves an analysis of the minimum distance between, for example, consecutive zeros of the product of the polynomials L α n L α+t n L α+2 n as t varies continuously between 0 and 2. Interesting work in a related context has been done in [6,7,13] and [14]. The interlacing property of the zeros of classical orthogonal polynomials, such as the Jacobi polynomials, has been used to develop new methods for approximating the finite Hilbert tranform (cf.…”

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confidence: 99%

Interlacing of zeros of shifted sequences of one-parameter orthogonal polynomials

Driver

Jordaan

2007

Numer. Math.

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confidence: 99%

Interlacing of zeros of shifted sequences of one-parameter orthogonal polynomials

Driver

Jordaan

2007

Numer. Math.

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“…For continuous load data, Lagrange interpolation (Criscuolo et al, 1984) is used to fill the vacancy and bad data, which can play a good repair effect. For the data points that need to be filled, m normal data points adjacent to the point are selected as samples to calculate the Lagrange interpolation formula:…”

Section: Load Data Preprocessingmentioning

confidence: 99%

Customer Load Forecasting Method Based on the Industry Electricity Consumption Behavior Portrait

Guan

Zhang

et al. 2021

Front. Energy Res.

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With the dramatic increase of energy demand and the continuous increase of power system operation pressure, higher requirements are put forward for the development of power grid planning and optimization operation. It is important for the refinement of distribution network planning to deeply extract the characteristics of user load. First, the process of load characteristic analysis method from the user level to the industry level is proposed, which achieves the division of electricity consumption patterns of various industries, thus building a panoramic portrait of industry electricity consumption behavior. Then, by expanding the information filled in by traditional customers, the feature vector of each user is extracted, and the users' industry electricity consumption patterns are used as the label. Therefore, a method for identifying the electricity consumption pattern of the customer based on the BB-stacking model fusion framework is proposed, which yields the preliminary forecast results of customer load based on the actual load accounting results of the customers. Finally, comparative simulations with different methods verify the effectiveness of the proposed algorithm, which can provide prominent guidance for the actual distribution network planning work.

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“…Moreover, we consider the Lagrange polynomial interpolating a function f at the zeros ofpm(v ~' -~) pm(v-~'~) and at the points _+ 1 (Theorem 2.3). This is a process of extended interpolation (see [1], [2], [3], [4]). …”

Section: M(v"-~ X) = [~'~Y_o X Pk(v ~'-~' X) -1mentioning

confidence: 99%

Some nodes matrices appearing in the numerical analysis for singular integral equations

Mastroianni

Prößdorf²

1994

BIT

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Abstract.Let {p~,(w)} be the sequence of Jacobi polynomials corresponding to the weight w(x) = (1 -x)~(1 + x) p, 0 < e, fl hold uniformly with respect to k and ra (Theorem 2. t). A similar result holds in the case c~ + fl = 1. Moreover, approximation properties of the Lagrange polynomial interpolating a function at the zeros of pm(w)pm(w-1) and at + 1 are studied (Theorem 2.3). These results have a crucial role in the error analysis of quadrature methods for solving Cauchy singular integral equations on the interval (-1, 1) [6].

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Uniform convergence of derivatives of extended Lagrange interpolation

Abstract: The authors construct some extended interpolation formulae to approximate the derivatives of a function in uniform norm. They prove theorems on uniform convergence and give estimates of pointwise type and of simultaneous approximation

Cited by 12 publications

References 20 publications

Interlacing of zeros of shifted sequences of one-parameter orthogonal polynomials

Interlacing of zeros of shifted sequences of one-parameter orthogonal polynomials

Customer Load Forecasting Method Based on the Industry Electricity Consumption Behavior Portrait

Some nodes matrices appearing in the numerical analysis for singular integral equations

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