scholarly journals Dynamic inverse problem for Jacobi matrices

2019 ◽  
Vol 13 (3) ◽  
pp. 431-447 ◽  
Author(s):  
Alexandr Mikhaylov ◽  
◽  
Victor Mikhaylov ◽  
Keyword(s):  
Inverse Problem ◽  
Jacobi Matrices ◽  
Dynamic Inverse ◽  
Dynamic Inverse Problem

scholarly journals On an application of the Boundary control method to classical moment problems.

2021 ◽  
Vol 2092 (1) ◽  
pp. 012002
Author(s):  
A S Mikhaylov ◽  
V S Mikhaylov
Keyword(s):  
Dynamical System ◽  
Inverse Problem ◽  
Boundary Control ◽  
Control Method ◽  
Jacobi Matrices ◽  
Moment Problems ◽  
Control Approach ◽  
Boundary Control Method ◽  
Dynamic Inverse ◽  
Dynamic Inverse Problem

Abstract We establish relationships between the classical moments problems which are problems of a construction of a measure supported on a real line, on a half-line or on an interval from prescribed set of moments with the Boundary control approach to a dynamic inverse problem for a dynamical system with discrete time associated with Jacobi matrices. We show that the solution of corresponding truncated moment problems is equivalent to solving some generalized spectral problems.

scholarly journals Dynamic inverse problem solution using a kalman filter smoother for neuronal activity estimation

TecnoLógicas ◽  
2011 ◽  
pp. 33 ◽  
Author(s):  
Eduardo Giraldo-Suárez ◽  
Jorge I. Padilla-Buriticá ◽  
César G. Castellanos-Domínguez
Keyword(s):  
Inverse Problem ◽  
Kalman Filter ◽  
Neuronal Activity ◽  
Problem Solution ◽  
Inverse Problem Solution ◽  
Dynamic Inverse ◽  
Activity Estimation ◽  
Dynamic Inverse Problem

En este artículo se presenta un método de estimación de la actividad neuronal sobre el cerebro usando un filtro de Kalman con suavizado, que tiene en cuenta en la solución del problema inverso, la variabilidad dinámica de la serie de tiempo. Este método es aplicado sobre un modelo realista de la cabeza, calculado con elementos finitos de frontera. Se presenta un análisis comparativo entre diferentes métodos de estimación y el método propuesto sobre señales EEG simuladas para diferentes condiciones de relación señal a ruido. La solución del problema inverso se hace utilizando computación de alto desempeño y se presenta una evaluación delcosto computacional para cada método. Como resultado, el filtro de Kalman con suavizado presenta un mejor desempeño en la tarea de estimación comparado con la solución estática regularizada, y la solución dinámica sin suavizado.

Inverse problems for finite Jacobi matrices and Krein–Stieltjes strings

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alexander Mikhaylov ◽  
Victor Mikhaylov
Keyword(s):  
Dynamical System ◽  
Inverse Problems ◽  
Jacobi Matrix ◽  
Jacobi Matrices ◽  
Unknown Parameters ◽  
Stieltjes String ◽  
Propagation Of Waves ◽  
Dynamic Inverse

Abstract We consider dynamic inverse problems for a dynamical system associated with a finite Jacobi matrix and for a system describing propagation of waves in a finite Krein–Stieltjes string. We offer three methods of recovering unknown parameters: entries of a Jacobi matrix in the first problem and point masses and distances between them in the second, from dynamic Dirichlet-to-Neumann operators. We also answer a question on a characterization of dynamic inverse data for these two problems.

Inverse problem about two-spectra for finite Jacobi matrices with zero diagonal

2016 ◽  
Vol 24 (6) ◽  
Author(s):  
Adil Huseynov
Keyword(s):  
Inverse Problem ◽  
Finite Order ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Jacobi Matrices ◽  
The Matrix ◽  
Explicit Procedure ◽  
Necessary And Sufficient

AbstractThe necessary and sufficient conditions for solvability of the inverse problem about two-spectra for finite order real Jacobi matrices with zero-diagonal elements are established. An explicit procedure of reconstruction of the matrix from the two-spectra is given.

scholarly journals On the M-matrix inverse problem for singular and symmetric Jacobi matrices

2012 ◽  
Vol 24 ◽  
Author(s):  
Angeles Carmona ◽  
Andres Encinas ◽  
Margarida Mitjana
Keyword(s):  
Inverse Problem ◽  
Jacobi Matrices ◽  
Matrix Inverse
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