scholarly journals Discrete-Continuous Symmetrized Sobolev Inner Products

2004 ◽  
Vol 82 (3) ◽  
pp. 309-331 ◽  
Author(s):  
María Isabel Bueno ◽  
Kil H. Kwon ◽  
Francisco Marcellán
Keyword(s):  
Inner Products ◽  
Sobolev Inner Products

scholarly journals On computational aspects of discrete Sobolev inner products on the unit circle

2013 ◽  
Vol 223 ◽  
pp. 452-460 ◽  
Author(s):  
Kenier Castillo ◽  
Lino G. Garza ◽  
Francisco Marcellán
Keyword(s):  
Unit Circle ◽  
Inner Products ◽  
Computational Aspects ◽  
Sobolev Inner Products

scholarly journals Continuous symmetrized Sobolev inner products of order N (I)

2005 ◽  
Vol 306 (1) ◽  
pp. 83-96 ◽  
Author(s):  
M. Isabel Bueno ◽  
Francisco Marcellán ◽  
Jorge Sánchez-Ruiz
Keyword(s):  
Inner Products ◽  
Sobolev Inner Products

scholarly journals On polynomials orthogonal with respect to certain Sobolev inner products

1991 ◽  
Vol 65 (2) ◽  
pp. 151-175 ◽  
Author(s):  
A Iserles ◽  
P.E Koch ◽  
S.P Nørsett ◽  
J.M Sanz-Serna
Keyword(s):  
Inner Products ◽  
Sobolev Inner Products

scholarly journals Sobolev Gradients for the Möbius Energy

2021 ◽  
Author(s):  
Philipp Reiter ◽  
Henrik Schumacher
Keyword(s):  
Optimization Methods ◽  
Inner Product ◽  
Stationary Points ◽  
Inner Products ◽  
Sobolev Gradients ◽  
Gradient Based ◽  
Standard Techniques ◽  
Sobolev Inner Products

AbstractAiming to optimize the shape of closed embedded curves within prescribed isotopy classes, we use a gradient-based approach to approximate stationary points of the Möbius energy. The gradients are computed with respect to Sobolev inner products similar to the $$W^{3/2,2}$$ W 3 / 2 , 2 -inner product. This leads to optimization methods that are significantly more efficient and robust than standard techniques based on $$L^2$$ L 2 -gradients.

scholarly journals Boundedness properties for Sobolev inner products

2003 ◽  
Vol 122 (1) ◽  
pp. 97-111 ◽  
Author(s):  
M. Castro ◽  
A.J. Durán
Keyword(s):  
Inner Products ◽  
Sobolev Inner Products

scholarly journals When are maps preserving semi-inner products linear?

2021 ◽  
Author(s):  
Paweł Wójcik
Keyword(s):  
Hilbert Space ◽  
Infinite Dimensions ◽  
Normed Spaces ◽  
Linear Isometry ◽  
Inner Products ◽  
Finite Dimensional ◽  
Uniformly Smooth ◽  
Non Linear ◽  
Extra Assumption ◽  
Continuous Injection

AbstractWe observe that every map between finite-dimensional normed spaces of the same dimension that respects fixed semi-inner products must be automatically a linear isometry. Moreover, we construct a uniformly smooth renorming of the Hilbert space $$\ell _2$$ ℓ 2 and a continuous injection acting thereon that respects the semi-inner products, yet it is non-linear. This demonstrates that there is no immediate extension of the former result to infinite dimensions, even under an extra assumption of uniform smoothness.

Support Vector Machines V: Exploiting Inner Products

NIR news ◽  
2005 ◽  
Vol 16 (3) ◽  
pp. 4-6 ◽  
Author(s):  
Tom Fearn ◽  
Donald J. Dahm
Keyword(s):  
Support Vector Machines ◽  
Support Vector ◽  
Inner Products ◽  
Vector Machines
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