Loaded differential equations and linear inverse problems for elliptic equations

2020 ◽  
pp. 1-19
Author(s):  
A.I. Kozhanov ◽  
T. N. Shipina
Keyword(s):  
Inverse Problems ◽  
Differential Equations ◽  
Elliptic Equations ◽  
Linear Inverse Problems

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

scholarly journals AMP-Inspired Deep Networks for Sparse Linear Inverse Problems

2017 ◽  
Vol 65 (16) ◽  
pp. 4293-4308 ◽  
Author(s):  
Mark Borgerding ◽  
Philip Schniter ◽  
Sundeep Rangan
Keyword(s):  
Inverse Problems ◽  
Linear Inverse Problems ◽  
Deep Networks

scholarly journals The Regularized Weak Functional Matching Pursuit for linear inverse problems

2019 ◽  
Vol 27 (3) ◽  
pp. 317-340 ◽  
Author(s):  
Max Kontak ◽  
Volker Michel
Keyword(s):  
Inverse Problems ◽  
Matching Pursuit ◽  
A Priori ◽  
Computation Time ◽  
Point Of View ◽  
Computational Point ◽  
Linear Inverse Problems ◽  
Infinite Dimensional ◽  
Frame Condition ◽  
Ill Posed

Abstract In this work, we present the so-called Regularized Weak Functional Matching Pursuit (RWFMP) algorithm, which is a weak greedy algorithm for linear ill-posed inverse problems. In comparison to the Regularized Functional Matching Pursuit (RFMP), on which it is based, the RWFMP possesses an improved theoretical analysis including the guaranteed existence of the iterates, the convergence of the algorithm for inverse problems in infinite-dimensional Hilbert spaces, and a convergence rate, which is also valid for the particular case of the RFMP. Another improvement is the cancellation of the previously required and difficult to verify semi-frame condition. Furthermore, we provide an a-priori parameter choice rule for the RWFMP, which yields a convergent regularization. Finally, we will give a numerical example, which shows that the “weak” approach is also beneficial from the computational point of view. By applying an improved search strategy in the algorithm, which is motivated by the weak approach, we can save up to 90  of computation time in comparison to the RFMP, whereas the accuracy of the solution does not change as much.

Inverse Problems for Partial Differential Equations

2012 ◽  
Vol 9 (1) ◽  
pp. 611-659
Author(s):  
Martin Hanke-Bourgeois ◽  
Andreas Kirsch ◽  
William Rundell ◽  
Matti Lassas
Keyword(s):  
Partial Differential Equations ◽  
Inverse Problems ◽  
Differential Equations ◽  
Partial Differential
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