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02-08-2019 | Original Paper | Issue 3/2020

Two-step inexact Newton-type method for inverse singular value problems

Journal:: Numerical Algorithms > Issue 3/2020

Authors:: Wei Ma, Xiao-shan Chen

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Important notes

The research of Wei Ma was partially supported by the Special Project Grant of Nanyang Normal University (ZX2014078).

The research of Xiao-shan Chen was partially supported by National Natural Science Foundations of China (11771159, U1811464).

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Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Abstract

In this paper, based on the two-step Newton iterative procedure, we propose a two-step inexact Newton-type method for solving inverse singular value problems. Under some mild assumptions, our results show that the two-step inexact Newton-type method is super quadratically convergent. Numerical implementations demonstrate the effectiveness of the new method.

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Alonso, P., Flores-Becerra, G., Vidal, A.M.: Sequential and parallel algorithms for the inverse Toeplitz singular value problem. Proc CSC, pp. 91–96 (2006)

Bai, Z.J., Chu, Delin, Sun, D.F.: A dual optimization approach to inverse quadratic eigenvalue problems with partial eigenstructure. SIAM J. Sci. Comput. 29 (6), 2531–2561 (2007) CrossRefMathSciNetMATH

Bai, Z.J., Jin, X.Q., Vong, S.W.: On some inverse singular value problems with Toeplitz-related structure. Numerical Algebra, Control and Optimization 2, 187–192 (2012) CrossRefMathSciNetMATH

Bai, Z.J., Morini, B., Xu, S.F.: On the local convergence of an iterative approach for inverse singular value problems. J. Comput. Appl. Math. 198, 344–360 (2007) CrossRefMathSciNetMATH

Bai, Z.J., Xu, S.F.: An inexact Newton-type method for inverse singular value problems. Linear Algebra Appl. 429, 527–547 (2008) CrossRefMathSciNetMATH

Chen, X.S., Sun, H.W.: On the unsolvability for inverse singular vlaue problems almost everywhere. Linear and Multilinear Algebra 67, 987–994 (2019) CrossRefMathSciNetMATH

Chen, X.S., Wen, C.T., Sun, H.W.: Two-step Newton type method for solving inverse eigenvalue problems. Numer. Linear Algebra Appl. https://doi.org/10.1002/nla.e2185

Chu, M.T.: Numerical methods for inverse singular value problems. SIAM J. Numer. Anal. 29, 885–903 (1992) CrossRefMathSciNetMATH

Chu, M.T., Golub, G.H.: Structured inverse eigenvalue problems. Acta Numer. 11, 1–71 (2002) CrossRefMathSciNetMATH

10.

Chu, M.T., Golub, G.H.: Inverse Eigenvalue Problems: Theory, Algorithms, and Applications. Oxford University Press, Oxford (2005) CrossRefMATH

11.

Flores-Becerra, G., Garcia, V.M., Vidal, A.M.: Parallelization of a method for the solution of the inverse additive singular value problem. WSEAS Transactions on Mathematics 5, 81–88 (2006) MathSciNet

12.

Friedland, S., Nocedal, J., Overton, M.L.: The formulation and analysis of numerical methods for inverse eigenvalue problems. SIAM J. Numer. Anal. 24, 634–667 (1987) CrossRefMathSciNetMATH

13.

Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore (1996) MATH

14.

Ma, W., Bai, Z.J.: A regularized directional derivative-based Newton method for inverse singular value problems. Inverse Prob. 28, 125001(24pp) (2012) CrossRefMathSciNetMATH

15.

Montaño, E., Salas, M., Soto, R.L.: Nonnegative matrices with prescribed extremal singular values. Comput. Math. Appl. 56, 30–42 (2008) CrossRefMathSciNetMATH

16.

Montaño, E., Salas, M., Soto, R.L.: Positive matrices with prescribed singular values. Proyecciones 27, 289–305 (2008) MATHMathSciNet

17.

Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York (1970) MATH

18.

Politi, T.: A discrete approach for the inverse singular value problem in some quadratic group. Lecture Notes in Comput. Sci. 2658, 121–130 (2003) CrossRefMathSciNetMATH

19.

Queiró, J.F.: An inverse problem for singular values and the Jacobian of the elementary symmetric functions. Linear Algebra Appl. 197–198, 277–282 (1994) CrossRefMathSciNetMATH

20.

Saad, Y.: Iterative Methods for Sparse Linear Systems. PWS Publishing Company, Boston (1996) MATH

21.

Saunders, C., Hu, J., Christoffersen, C., Steer, M.: Inverse singular value method for enforcing passivity in reduced-order models of distributed structures for transient and steady-state simulation. IEEE Trans. Microwave Theory and Techniques 59, 837–847 (2011) CrossRef

22.

Stewart, G.W., Sun, J.G.: Matrix Perturbation Theory. Academic, San Diego (1990) MATH

23.

Tropp, J.A., Dhillon, I.S., Heath, R.W.: Finite-step algorithms for constructing optimal CDMA signature sequences. IEEE Trans. Inform. Theory 50, 2916–2921 (2004) CrossRefMathSciNetMATH

24.

Vong, S.W., Bai, Z.J., Jin, X.Q.: A Ulm-like method for inverse singular value problems. SIAM J. Matrix. Anal. Appl. 32, 412–429 (2011) CrossRefMathSciNetMATH

25.

Xu, S.F.: An Introduction to Inverse Algebric Eigenvalue Problems. Peking University Press and Vieweg Publishing, Beijing (1998)

26.

Yuan, S.F., Liao, A.P., Yao, G.Z.: Parameterized inverse singular value problem for anti-bisymmetric matrices. Numer. Algorithms 60, 501–522 (2012) CrossRefMathSciNetMATH

Title: Two-step inexact Newton-type method for inverse singular value problems
Authors:: Wei Ma
Xiao-shan Chen
Publication date: 02-08-2019
DOI: https://doi.org/10.1007/s11075-019-00783-x
Publisher: Springer US
Journal: Numerical Algorithms
Issue 3/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265

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Abstract

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