On numerical stability of randomized projection functional algorithms

T. E. Bulgakova; A. V. Voytishek

doi:10.1080/03610918.2019.1677914

On numerical stability of randomized projection functional algorithms

Результат исследования: Научные публикации в периодических изданиях › статья

Аннотация

In this paper, the application of randomized projection functional algorithms for numerical approximation of solutions of Fredholm equations of the second kind is discussed. Special attention is paid to the problems of numerical stability of the used orthonormal functional bases. The numerical instability of the randomized projection functional algorithm is noticed for the simple test one-dimensional equation and for the Hermite orthonormal basis.

Язык оригинала	английский
Журнал	Communications in Statistics: Simulation and Computation
DOI	https://doi.org/10.1080/03610918.2019.1677914
Состояние	Опубликовано - 15 окт 2019

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Bulgakova, T. E., & Voytishek, A. V. (2019). On numerical stability of randomized projection functional algorithms. Communications in Statistics: Simulation and Computation. https://doi.org/10.1080/03610918.2019.1677914

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title = "On numerical stability of randomized projection functional algorithms",

abstract = "In this paper, the application of randomized projection functional algorithms for numerical approximation of solutions of Fredholm equations of the second kind is discussed. Special attention is paid to the problems of numerical stability of the used orthonormal functional bases. The numerical instability of the randomized projection functional algorithm is noticed for the simple test one-dimensional equation and for the Hermite orthonormal basis.",

keywords = "Integral Fredholm equations of the second kind, Lebesgue constant, Numerical approximation, Numerical stability of the used orthonormal bases, Randomized projection and mesh functional algorithms",

author = "Bulgakova, {T. E.} and Voytishek, {A. V.}",

year = "2019",

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day = "15",

doi = "10.1080/03610918.2019.1677914",

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AU - Bulgakova, T. E.

AU - Voytishek, A. V.

PY - 2019/10/15

Y1 - 2019/10/15

N2 - In this paper, the application of randomized projection functional algorithms for numerical approximation of solutions of Fredholm equations of the second kind is discussed. Special attention is paid to the problems of numerical stability of the used orthonormal functional bases. The numerical instability of the randomized projection functional algorithm is noticed for the simple test one-dimensional equation and for the Hermite orthonormal basis.

AB - In this paper, the application of randomized projection functional algorithms for numerical approximation of solutions of Fredholm equations of the second kind is discussed. Special attention is paid to the problems of numerical stability of the used orthonormal functional bases. The numerical instability of the randomized projection functional algorithm is noticed for the simple test one-dimensional equation and for the Hermite orthonormal basis.

KW - Integral Fredholm equations of the second kind

KW - Lebesgue constant

KW - Numerical approximation

KW - Numerical stability of the used orthonormal bases

KW - Randomized projection and mesh functional algorithms

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U2 - 10.1080/03610918.2019.1677914

DO - 10.1080/03610918.2019.1677914

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JO - Communications in Statistics Part B: Simulation and Computation

JF - Communications in Statistics Part B: Simulation and Computation

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Доступ к документу

10.1080/03610918.2019.1677914

Link to publication in Scopus