Determining the Resistors in a Network

Curtis, Edward B.; Morrow, James

doi:10.1137/0150055

Cited by 72 publications

(65 citation statements)

References 3 publications

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“…Similar results may be obtained for other types of circular networks (e.g., where the ou ter conductors are not present), which are discussed in Section 9. In [4] and [3] we solved the four problems above for square resistor networks. The methods presented hère are simplifications of those of [4] and [3].…”

Section: The Potential U Détermines a Current I U (P) Into Each Boundmentioning

confidence: 99%

Finding the conductors in circular networks from boundary measurements

Curtis¹,

Mooers²,

Morrow³

1994

ESAIM: M2AN

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Section: The Potential U Détermines a Current I U (P) Into Each Boundmentioning

confidence: 99%

Finding the conductors in circular networks from boundary measurements

Curtis¹,

Mooers²,

Morrow³

1994

ESAIM: M2AN

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“…That is, we can decide whether there is an increase of traffic somewhere in the network or not. While this is only a uniqueness theorem, nevertheless, we can effectively compute the actual weights from the knowledge of the Dirichlet data for convenient choices of the input Neumann data in a way similar to that done in [21] and [23] for lattices. Similarly, the Green function of this Neumann boundary value problem can be represented by an explicit matrix.…”

Section: The Weighted Graph Modelmentioning

confidence: 99%

Network Tomography

Gavilanez¹,

Berenstein²,

Baras³

2005

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ISR develops, applies and teaches advanced methodologies of design and analysis to solve complex, hierarchical, heterogeneous and dynamic problems of engineering technology and systems for industry and government. ISR is a permanent institute of the University of Maryland AbstractWhile conventional tomography is associated to the Radon transform in Euclidean spaces, electrical impedance tomography or EIT is associated to the Radon transform in the hyperbolic plane. We discuss some recent work on network tomography that can be associated to a problem similar to EIT on graphs and indicate how in some sense it may be also associated to the Radon transform on trees.

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“…The idea of layer stripping based on a different Ricatti equation than (1.10) has been used in electric impedance tomography in [29]. Furthermore, the method has been extended to imaging a rectangular resistor network in [14]. The main problem of these algorithms is the stability issue for the high-frequency modes.…”

Section: Introductionmentioning

confidence: 99%

A multiscattering series for impedance tomography in layered media

Borcea

Ortiz

1999

Inverse Problems

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Abstract. We introduce an inversion algorithm for tomographic images of layered media. The algorithm is based on a multiscattering series expansion of the Green function that, unlike the Born series, converges unconditionally. Our inversion algorithm obtains images of the medium that improves iteratively as we use more and more terms in the multiscattering series. We present the derivation of the multiscattering series, formulate the inversion algorithm and demonstrate its performance through numerical experiments.

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Determining the Resistors in a Network

Cited by 72 publications

References 3 publications

Finding the conductors in circular networks from boundary measurements

Finding the conductors in circular networks from boundary measurements

Network Tomography

A multiscattering series for impedance tomography in layered media

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