Sobolev-orthogonal systems of functions and some of their applications
II Sharapudinov - Russian Mathematical Surveys, 2019 - iopscience.iop.org
Abstract Systems of functions are considered which are associated with a given orthogonal
system and are orthogonal with respect to an inner product of Sobolev type involving terms …
system and are orthogonal with respect to an inner product of Sobolev type involving terms …
The curse of unrolling: Rate of differentiating through optimization
Computing the Jacobian of the solution of an optimization problem is a central problem in
machine learning, with applications in hyperparameter optimization, meta-learning …
machine learning, with applications in hyperparameter optimization, meta-learning …
Ортогональные по Соболеву системы функций и некоторые их приложения
ИИ Шарапудинов - Успехи математических наук, 2019 - mathnet.ru
Рассмотрены системы функций, которые являются ортогональными относительно
скалярных произведений типа Соболева, содержащих слагаемые с массами …
скалярных произведений типа Соболева, содержащих слагаемые с массами …
Coherent pairs of measures of the second kind on the real line and Sobolev orthogonal polynomials. An application to a Jacobi case
GA Marcato, F Marcellán, AS Ranga… - Studies in Applied …, 2023 - Wiley Online Library
The aim here is to consider the orthogonal polynomials S n (ν 0, ν 1, s; x) S_n(ν_0,ν_1,s;x)
with respect to an inner product of the type⟨ f, g⟩ s=∫ f (x) g (x) d ν 0 (x)+ s∫ f′(x) g′(x) d …
with respect to an inner product of the type⟨ f, g⟩ s=∫ f (x) g (x) d ν 0 (x)+ s∫ f′(x) g′(x) d …
[HTML][HTML] Approximation via gradients on the ball. The Zernike case
In this work, we deal in ad dimensional unit ball equipped with an inner product constructed
by adding a mass point at zero to the classical ball inner product applied to the gradients of …
by adding a mass point at zero to the classical ball inner product applied to the gradients of …
Coherent pairs of moment functionals of the second kind and associated orthogonal polynomials and Sobolev orthogonal polynomials
MH Suni, GA Marcato, F Marcellán… - Journal of Mathematical …, 2023 - Elsevier
Given a pair of quasi-definite moment functionals {v 0, v 1} we introduce the concept of
coherence of the second kind in terms of an algebraic relation that the corresponding …
coherence of the second kind in terms of an algebraic relation that the corresponding …
Matrix biorthogonal polynomials on the real line: Geronimus transformations
G Ariznabarreta, JC García-Ardila, M Mañas… - Bulletin of …, 2019 - World Scientific
In this paper, Geronimus transformations for matrix orthogonal polynomials in the real line
are studied. The orthogonality is understood in a broad sense, and is given in terms of a …
are studied. The orthogonality is understood in a broad sense, and is given in terms of a …
Approximation by polynomials in Sobolev spaces associated with classical moment functionals
JC García-Ardila, ME Marriaga - Numerical Algorithms, 2024 - Springer
Let u be a moment functional associated with the Hermite, Laguerre, or Jacobi classical
orthogonal polynomials. We study approximation by polynomials in H r (u), the Sobolev …
orthogonal polynomials. We study approximation by polynomials in H r (u), the Sobolev …
One-step estimation of differentiable Hilbert-valued parameters
A Luedtke, I Chung - The Annals of Statistics, 2024 - projecteuclid.org
One-step estimation of differentiable Hilbert-valued parameters Page 1 The Annals of Statistics
2024, Vol. 52, No. 4, 1534–1563 https://doi.org/10.1214/24-AOS2403 © Institute of …
2024, Vol. 52, No. 4, 1534–1563 https://doi.org/10.1214/24-AOS2403 © Institute of …
Системы функций, ортогональные по Соболеву, ассоциированные с ортогональной системой
ИИ Шарапудинов - Известия Российской академии наук. Серия …, 2018 - mathnet.ru
В ряде наших работ [1]–[5] были введены так называемые смешанные ряды по
классическим ортогональным полиномам, частичные суммы которых обладают …
классическим ортогональным полиномам, частичные суммы которых обладают …