A Parallel Algorithm for the Solution of the Deconvolution Problem on Heterogeneous Networks

Alonso, Pedro; Vidal, Antonio M.; Lastovetsky, Alexey

doi:10.1109/clustr.2006.311908

Cited by 2 publications

(2 citation statements)

References 17 publications

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“…0 are the singular values of M. Partition P by P = [P (1) , P (2) ], where P (1) ∈ M m×n and P (2) ∈ M m×(m−n) . Let U ∈ O(m + n) be defined by…”

Section: A Regularized Directional Derivative-based Newton Methodsmentioning

confidence: 99%

“…The inverse problem of reconstructing a matrix from the given singular values, i.e. the inverse singular value problem (ISVP), has growing importance in many applications such as the optimal sequence design for direct-spread code division multiple access [39], the passivity enforcement in nonlinear circuit simulation [33], the constructions of Toeplitz-related matrices from prescribed singular values [1,2,13], the inverse problem in some quadratic group [27], and the construction of nonnegative, positive and anti-bisymmetric matrices with prescribed singular values [23,24,42] and others [30].…”

Section: Introductionmentioning

confidence: 99%

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A regularized directional derivative-based Newton method for inverse singular value problems

Ma¹,

Bai²

2012

Inverse Problems

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In this paper, we give a regularized directional derivative-based Newton method for solving the inverse singular value problem. The proposed method is also globalized by employing the directional derivative-based Wolfe line search conditions. Under some mild assumptions, The global and quadratic convergence of our method is established. To improve the practical effectiveness, we also propose a hybrid method for solving the inverse singular value problem. We show that the hybrid method converges locally quadratically and globally in the sense that a stationary point of a merit function for the inverse singular value problem is computed. Numerical tests demonstrate that the proposed hybrid method is very effective for solving the inverse singular value problem with distinct and multiple singular values.

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“…0 are the singular values of M. Partition P by P = [P (1) , P (2) ], where P (1) ∈ M m×n and P (2) ∈ M m×(m−n) . Let U ∈ O(m + n) be defined by…”

Section: A Regularized Directional Derivative-based Newton Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A regularized directional derivative-based Newton method for inverse singular value problems

Ma¹,

Bai²

2012

Inverse Problems

View full text Add to dashboard Cite

show abstract