CONSTRUCTION OF FULL H-MATRICES WITH THE GIVEN EIGENVALUES BASED ON THE GIVENS MATRICES

Jicheng Li; Guiling Zhang; Nana Wang; Guo Li; Chengyi Zhang

doi:10.11948/2018.81

2018 Volume 8 Issue 1

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Jicheng Li, Guiling Zhang, Nana Wang, Guo Li, Chengyi Zhang. CONSTRUCTION OF FULL H-MATRICES WITH THE GIVEN EIGENVALUES BASED ON THE GIVENS MATRICES[J]. Journal of Applied Analysis & Computation, 2018, 8(1): 81-104. doi: 10.11948/2018.81

Citation:

Jicheng Li, Guiling Zhang, Nana Wang, Guo Li, Chengyi Zhang. CONSTRUCTION OF FULL H-MATRICES WITH THE GIVEN EIGENVALUES BASED ON THE GIVENS MATRICES[J]. Journal of Applied Analysis & Computation, 2018, 8(1): 81-104. doi: 10.11948/2018.81

CONSTRUCTION OF FULL H-MATRICES WITH THE GIVEN EIGENVALUES BASED ON THE GIVENS MATRICES

1 School of Mathematics and Statistics, Xi'an Jiaotong University, No. 28, Xianning West Road, 710049 Xi'an, China;
2 School of Mathematics and Statistics, Shenzhen University, Nanhai Ave 3688, 518060 Shenzhen, China;
3 School of Science, Xi'an ploytechnic University, No.19 Jinhua South Road, 710048 Xi'an, China

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Abstract

Abstract

The inverse eigenvalue problem is about how to construct a desired matrix whose spectrum is the given number set. In this paper, in view of the Givens matrices, we prove that there exist three classes of full H-matrices which include strictly diagonally dominant full matrix, α-strictly diagonally dominant full matrix and α-double strictly diagonally dominant full matrix, and their spectrum are all the given number set. In addition, we design some numerical algorithms to explain how to construct the above-mentioned full H-matrices.
- Full matrix /
- H-matrix /
- strictly diagonally dominant matrix /
- α-strictly diagonally dominant matrix /
- α-double strictly diagonally dominant matrix /
- givens matrix
MSC: 65F10;65F15;15A09

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References

[1]	M. T. Chu and G. H. Golub, Inverse Eigenvalue Problems:Theory, Algorithms, and Applications, Oxford University Press, USA, 2005. Google Scholar
[2]	M. T. Chu, F. Diele and S. Ragni, On the inverse problem of constructing symmetric pentadiagonal Toeplitz matrices from their three largest eigenvalues, Inverse Probl., 2005, 21(6), 1879-1894. Google Scholar
[3]	T. B. Gan and T. Z. Huang, Simple criteria for nonsingular H-matrices, Linear Algebra Appl., 2003. DOI:10.1016/S0024-3795(03)00646-3. Google Scholar
[4]	K. Ghanbari, A survey on inverse and generalized inverse eigenvalue problems for Jacobi matrices, Appl. Math. Comput., 2008, 195(2), 355-363. Google Scholar
[5]	S. G. Hwang and S. S. Pyo, The inverse eigenvalue problem for symmetric doubly stochastic matrices, Linear Algebra Appl., 2004. DOI:10.1016/S0024-3795(03)00366-5. Google Scholar
[6]	Z. Y. Liu, Y. L. Zhang, C. Ferreira and R. Ralha, On inverse eigenvalue problems for block Toeplitz matrices with Toeplitz blocks, Appl. Math. Comput., 2010, 216(6), 1819-1830. Google Scholar
[7]	J. Z. Liu and Y. Q. Huang, Some properties on Schur complements of Hmatrices and diagonally dominant matrices, Linear Algebra Appl., 2004. DOI:10.1016/j.laa.2004.04.012. Google Scholar
[8]	A. M. Nazari and F. Sherafat, On the inverse eigenvalue problem for nonnegative matrices of order two to five, Linear Algebra Appl., 2012, 436(7), 1771-1790. Google Scholar
[9]	J. Peng, X. Y. Hu and L. Zhang, A kind of inverse eigenvalue problems of Jacobi matrix, Appl. Math. Comput., 2006, 175(2), 1543-1555. Google Scholar
[10]	P. Pango and B. Champagne, On the efficient use of Givens rotations in SVDbased subspace tracking algorithms, Signal Processing, 1999, 74(3), 253-277. Google Scholar
[11]	W. Rudin, Principles of mathematical analysis, McGraw-Hill Education, USA, 1976. Google Scholar
[12]	J. J. Rotman, Advanced Modern Algebra, Prentice Hall, USA, 2003. Google Scholar
[13]	H. Šmigoc, The inverse eigenvalue problem for nonnegative matrices, Linear Algebra Appl., 2004. DOI:10.1016/j.laa.2004.03.036. Google Scholar
[14]	X. Q. Wu and E. X. Jiang, A new algorithm on the inverse eigenvalue problem for double dimensional Jacobi matrices, Linear Algebra Appl., 2012, 437(7), 1760-1770. Google Scholar
[15]	X. Q. Wu, A divide and conquer algorithm on the double dimensional inverse eigenvalue problem for Jacobi matrices, Appl. Math. Comput., 2012, 219(8), 3840-3846. Google Scholar
[16]	Y. Wei and H. Dai, An inverse eigenvalue problem for Jacobi matrix, Appl. Math. Comput., 2015. DOI:10.1016/j.amc.2014.11.101. Google Scholar
[17]	Y. Wei, A Jacobi matrix inverse eigenvalue problem with mixed date, Linear Algebra Appl., 2013, 439(10), 2774-2783. Google Scholar
[18]	Y. Wei, Inverse eigenvalue problem of Jacobi matrix with mixed data, Linear Algebra Appl., 2015. DOI:10.1016/j.laa.2014.09.031. Google Scholar
[19]	R. Witu la, D. S lota and M. Kampik, Some properties of the full matrices, Appl. Math. Comput., 2012, 219(3), 1222-1231. Google Scholar