scholarly journals Random heat equation: Solutions by the stochastic adaptive interpolation method

1988 ◽  
Vol 16 (9) ◽  
pp. 759-766 ◽  
Author(s):  
N. Bellomo ◽  
L.M. de Socio ◽  
R. Monaco
Keyword(s):  
Heat Equation ◽  
Interpolation Method ◽  
Adaptive Interpolation

scholarly journals Mutual information for low-rank even-order symmetric tensor estimation

2020 ◽  
Author(s):  
Clément Luneau ◽  
Jean Barbier ◽  
Nicolas Macris
Keyword(s):  
Mutual Information ◽  
Finite Rank ◽  
Interpolation Method ◽  
Symmetric Tensor ◽  
Low Rank ◽  
Tensor Factorization ◽  
Adaptive Interpolation ◽  
Odd Order ◽  
Rank One ◽  
Even Order

Abstract We consider a statistical model for finite-rank symmetric tensor factorization and prove a single-letter variational expression for its asymptotic mutual information when the tensor is of even order. The proof applies the adaptive interpolation method originally invented for rank-one factorization. Here we show how to extend the adaptive interpolation to finite-rank and even-order tensors. This requires new non-trivial ideas with respect to the current analysis in the literature. We also underline where the proof falls short when dealing with odd-order tensors.

GEOMETRIC INTEGRATION BY SOLUTION INTERPOLATION

2009 ◽  
Vol 20 (02) ◽  
pp. 313-322
Author(s):  
PILWON KIM
Keyword(s):  
Differential Equation ◽  
Heat Equation ◽  
Exact Solutions ◽  
Standard Method ◽  
Interpolation Method ◽  
Nonlinear Heat Equation ◽  
Geometric Integration ◽  
Numerical Schemes ◽  
New Class ◽  
Geometric Integrators

Numerical schemes that are implemented by interpolation of exact solutions to a differential equation naturally preserve geometric properties of the differential equation. The solution interpolation method can be used for development of a new class of geometric integrators, which generally show better performances than standard method both quantitatively and qualitatively. Several examples including a linear convection equation and a nonlinear heat equation are included.

scholarly journals Content adaptive single image interpolation based super resolution of compressed images

2020 ◽  
Vol 10 (3) ◽  
pp. 3014
Author(s):  
Amanjot Singh ◽  
Jagroop Singh
Keyword(s):  
Interpolation Method ◽  
Super Resolution ◽  
Original Image ◽  
Single Image ◽  
Standard Methods ◽  
Compressed Images ◽  
Adaptive Interpolation ◽  
Image Super Resolution ◽  
Simulation Results ◽  
Content Adaptive

Image Super resolution is used to upscale the low resolution Images. It is also known as image upscaling .This paper focuses on upscaling of compressed images based on Interpolation techniques. A content adaptive interpolation method of image upscaling has been proposed. This interpolation based scheme is useful for single image based Super-resolution (SR) methods .The presented method works on horizontal, vertical and diagonal directions of an image separately and it is adaptive to the local content of an image. This method relies only on single image and uses the content of the original image only; therefore the proposed method is more practical and realistic. The simulation results have been compared to other standard methods with the help of various performance matrices like PSNR, MSE, MSSIM etc. which indicates the preeminence of the proposed method.

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