Computation of the resolvent matrix for the generalized bitangential Schur- and Caratheodory-Nevanlinna-Pick interpolation problems in the strictly completely indeterminate case

D. Z. Arov

doi:10.1007/bf01378775

Computation of the resolvent matrix for the generalized bitangential Schur- and Caratheodory-Nevanlinna-Pick interpolation problems in the strictly completely indeterminate case

Integral Equations and Operator Theory ◽

10.1007/bf01378775 ◽

1995 ◽

Vol 22 (3) ◽

pp. 253-272 ◽

Cited By ~ 4

Author(s):

D. Z. Arov

Keyword(s):

Resolvent Matrix ◽

Interpolation Problems ◽

Indeterminate Case

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Application of Atomic Functions to Interpolation Problems

Telecommunications and Radio Engineering ◽

10.1615/telecomradeng.v54.i11-12.20 ◽

2000 ◽

Vol 54 (11-12) ◽

pp. 23-37

Author(s):

Victor Filippovich Kravchenko ◽

Vladimir Alexeevich Rvachev

Keyword(s):

Interpolation Problems

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Signal Estimation, Scattering Theory and Interpolation Problems in One and Two Dimensions.

10.21236/ada168969 ◽

1986 ◽

Author(s):

Thomas Kailath

Keyword(s):

Scattering Theory ◽

Two Dimensions ◽

Signal Estimation ◽

Interpolation Problems

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End-to-End Learning of Variational Models and Solvers for the Resolution of Interpolation Problems

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) ◽

10.1109/icassp39728.2021.9414629 ◽

2021 ◽

Author(s):

R. Fablet ◽

L. Drumetz ◽

F. Rousseau

Keyword(s):

Variational Models ◽

Interpolation Problems ◽

End To End

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Optimal parameter selection in Weeks’ method for numerical Laplace transform inversion based on machine learning

Journal of Algorithms & Computational Technology ◽

10.1177/1748302621999621 ◽

2021 ◽

Vol 15 ◽

pp. 174830262199962

Author(s):

Patrick O Kano ◽

Moysey Brio ◽

Jacob Bailey

Keyword(s):

Laplace Transform ◽

Optimal Parameter ◽

Large Data ◽

Matrix Exponential ◽

Resolvent Matrix ◽

Data Set ◽

Network Training ◽

The Matrix ◽

The Laplace Transform ◽

Space Function

The Weeks method for the numerical inversion of the Laplace transform utilizes a Möbius transformation which is parameterized by two real quantities, σ and b. Proper selection of these parameters depends highly on the Laplace space function F( s) and is generally a nontrivial task. In this paper, a convolutional neural network is trained to determine optimal values for these parameters for the specific case of the matrix exponential. The matrix exponential eA is estimated by numerically inverting the corresponding resolvent matrix [Formula: see text] via the Weeks method at [Formula: see text] pairs provided by the network. For illustration, classes of square real matrices of size three to six are studied. For these small matrices, the Cayley-Hamilton theorem and rational approximations can be utilized to obtain values to compare with the results from the network derived estimates. The network learned by minimizing the error of the matrix exponentials from the Weeks method over a large data set spanning [Formula: see text] pairs. Network training using the Jacobi identity as a metric was found to yield a self-contained approach that does not require a truth matrix exponential for comparison.

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