Numerical Experiments on the Solution of the Inverse Additive Singular Value Problem

Flores-Becerra, Georgina; García, Víctor M.; Vidal, Antonio M.

doi:10.1007/11428831_3

Cited by 6 publications

(8 citation statements)

References 10 publications

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“…Suppose the given singular values 1 , 2 , … , n are all distinct. We see from Theorem 1 that if X = (S, U, V) ∈  is such that there exist n rows are independent in the n 2 × n matrix P defined by (8), then the positive definiteness of DH(⋅) • (DH (⋅)) * is guaranteed. Moreover, the positive definiteness conditions in Theorem 1 may be unnecessary in practice.…”

Section: Riemannian Inexact Newton-cg Methodsmentioning

confidence: 99%

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A Riemannian inexact Newton‐CG method for stochastic inverse singular value problems

Bai

2020

Numerical Linear Algebra App

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In this article, we consider the stochastic inverse singular value problem (ISVP) of constructing a stochastic matrix from the prescribed realizable singular values. We propose a Riemannian inexact Newton-CG method with various choices of forcing terms for solving the stochastic ISVP. We show the proposed method converges linearly or superlinearly for different forcing terms under some assumptions. We also extend the proposed method to the case of prescribed entries. Finally, we report some numerical results to demonstrate the effectiveness of the proposed method.

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Section: Riemannian Inexact Newton-cg Methodsmentioning

confidence: 99%

“…The ISVP arises in many applications such as structural health monitoring, code division multiple access system, quadratic group, transient circuit simulation 1‐4 . There are different structured ISVPs including the affine ISVP and the ISVP for Toeplitz‐related matrices, nonnegative, positive, and antibisymmetric matrices 5‐11 …”

Section: Introductionmentioning

confidence: 99%

A Riemannian inexact Newton‐CG method for stochastic inverse singular value problems

Bai

2020

Numerical Linear Algebra App

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“…Assume that w(z k ) = 0 for all k and each generalized Newton equation (12) can be solved inexactly such that the conditions (13) and (14) are satisfied. Suppose that Assumption 4.3 is satisfied and D is dense in R n .…”

Section: Convergence Analysismentioning

confidence: 99%

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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“…The same procedure is followed to compute A (4) , A (5) , ..., A (n) . The final result will be the unit lower triangular matrix A (n) , whose singular values are S * .…”

Section: Methods Based In Weyl's Conditions(we Method)mentioning

confidence: 99%

“…There exist several algorithms to solve this problem, such as MI, MIII, EP and FB [5], which are iterative Newton-like algorithms, with high computational cost (O(n 4 ) for MI, MIII and EP; and O(n 6 ) for FB). If the desired matrix must have a certain structure, the computational costs can be drastically reduced.…”

Section: Introductionmentioning

confidence: 99%

Efficient Parallel Algorithm for Constructing a Unit Triangular Matrix with Prescribed Singular Values

Flores-Becerra

García

Vidal

Lecture Notes in Computer Science

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The problem tackled in this paper is the parallel construction of a unit triangular matrix with prescribed singular values, when these fulfill Weyl's conditions [9]; this is a particular case of the Inverse Singular Value Problem. A sequential algorithm for this problem was proposed in [10] by Kosowsky and Smoktunowicz. In this paper parallel versions of this algorithm will be described, both for shared memory and distributed memory architectures. The proposed parallel implementation is better suited for the shared memory paradigm; this is confirmed by the numerical experiments; the shared memory version, reaches an efficiency over 90%, and reduces substantially the execution times compared with the sequential algorithm.

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Numerical Experiments on the Solution of the Inverse Additive Singular Value Problem

Cited by 6 publications

References 10 publications

A Riemannian inexact Newton‐CG method for stochastic inverse singular value problems

A Riemannian inexact Newton‐CG method for stochastic inverse singular value problems

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

Efficient Parallel Algorithm for Constructing a Unit Triangular Matrix with Prescribed Singular Values

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