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On some inverse singular value problems with Toeplitz-related structure
1. | School of Mathematical Sciences, Xiamen University, Xiamen 361005, China |
2. | Department of Mathematics, University of Macau, Macau, China, China |
References:
[1] |
Z. J. Bai, Inexact Newton methods for inverse eigenvalue problems,, Appl. Math. Comput., 172 (2006), 682.
doi: 10.1016/j.amc.2004.11.023. |
[2] |
Z. J. Bai, R. H. Chan and B. Morini, An inexact Cayley transform method for inverse eigenvalue problems,, Inverse Problems, 20 (2004), 1675.
doi: 10.1088/0266-5611/20/5/022. |
[3] |
Z. J. Bai and X. Q. Jin, A note on the Ulm-like method for inverse eigenvalue problems,, In, (2011), 1. Google Scholar |
[4] |
D. Bini and M. Capovani, Spectral and computational properties of band symmetric Toeplitz matrices,, Linear Algebra Appl., 52/53 (1983), 99.
|
[5] |
R. H. Chan, H. L. Chung and S. F. Xu, The inexact Newton-like method for inverse eigenvalue problem,, BIT, 43 (2003), 7.
doi: 10.1023/A:1023611931016. |
[6] |
X. S. Chen, A backward error for the inverse singular value problem,, J. Comput. Appl. Math., 234 (2010), 2450.
doi: 10.1016/j.cam.2010.03.003. |
[7] |
M. T. Chu, Numerical methods for inverse singular value problems,, SIAM J. Numer. Anal., 29 (1992), 885.
doi: 10.1137/0729054. |
[8] |
M. T. Chu, Inverse eigenvalue problems,, SIAM Rev., 40 (1998), 1.
doi: 10.1137/S0036144596303984. |
[9] |
M. T. Chu and G. H. Golub, Structured inverse eigenvalue problems,, Acta Numer., 11 (2002), 1.
doi: 10.1017/S0962492902000016. |
[10] |
M. T. Chu and G. H. Golub, "Inverse Eigenvalue Problems: Theory, Algorithms and Applications,", Oxford University Press, (2005).
doi: 10.1093/acprof:oso/9780198566649.001.0001. |
[11] |
F. Diele, T. Laudadio and N. Mastronardi, On some inverse eigenvalue problems with Toeplitz-related structure,, SIAM J. Matrix Anal. Appl., 26 (2004), 285.
doi: 10.1137/S0895479803430680. |
[12] |
S. Friedland, J. Nocedal and M. L. Overton, The formulation and analysis of numerical methods for inverse eigenvalue problems,, SIAM J. Numer. Anal., 24 (1987), 634.
doi: 10.1137/0724043. |
[13] |
A. Jain, "Fundamentals of Digital Image Processing,", Prentice-Hall, (1989). Google Scholar |
[14] |
E. Montaño, M. Salas and R. L. Soto, Nonnegative matrices with prescribed extremal singular values,, Comput. Math. Appl., 56 (2008), 30.
|
[15] |
E. Montaño, M. Salas and R. L. Soto, Positive matrices with prescribed singular values,, Proyecciones, 27 (2008), 289.
|
[16] |
W. P. Shen, C. Li and X. Q. Jin, A Ulm-like method for inverse eigenvalue problems,, Appl. Numer. Math., 61 (2011), 356.
doi: 10.1016/j.apnum.2010.11.001. |
[17] |
J. A. Tropp, I. S. Dhillon and R. W. Heath Jr., Finite-step algorithms for constructing optimal CDMA signature sequences,, IEEE Trans. Inform. Theory, 50 (2004), 2916.
doi: 10.1109/TIT.2004.836698. |
[18] |
S. W. Vong, Z. J. Bai and X. Q. Jin, An Ulm-like method for inverse singular value problems,, SIAM J. Matrix Anal. Appl., 32 (2011), 412.
doi: 10.1137/100815748. |
[19] |
S. F. Xu, "An Introduction to Inverse Eigenvalue Problems,", Peking University Press and Vieweg Publishing, (1998). Google Scholar |
show all references
References:
[1] |
Z. J. Bai, Inexact Newton methods for inverse eigenvalue problems,, Appl. Math. Comput., 172 (2006), 682.
doi: 10.1016/j.amc.2004.11.023. |
[2] |
Z. J. Bai, R. H. Chan and B. Morini, An inexact Cayley transform method for inverse eigenvalue problems,, Inverse Problems, 20 (2004), 1675.
doi: 10.1088/0266-5611/20/5/022. |
[3] |
Z. J. Bai and X. Q. Jin, A note on the Ulm-like method for inverse eigenvalue problems,, In, (2011), 1. Google Scholar |
[4] |
D. Bini and M. Capovani, Spectral and computational properties of band symmetric Toeplitz matrices,, Linear Algebra Appl., 52/53 (1983), 99.
|
[5] |
R. H. Chan, H. L. Chung and S. F. Xu, The inexact Newton-like method for inverse eigenvalue problem,, BIT, 43 (2003), 7.
doi: 10.1023/A:1023611931016. |
[6] |
X. S. Chen, A backward error for the inverse singular value problem,, J. Comput. Appl. Math., 234 (2010), 2450.
doi: 10.1016/j.cam.2010.03.003. |
[7] |
M. T. Chu, Numerical methods for inverse singular value problems,, SIAM J. Numer. Anal., 29 (1992), 885.
doi: 10.1137/0729054. |
[8] |
M. T. Chu, Inverse eigenvalue problems,, SIAM Rev., 40 (1998), 1.
doi: 10.1137/S0036144596303984. |
[9] |
M. T. Chu and G. H. Golub, Structured inverse eigenvalue problems,, Acta Numer., 11 (2002), 1.
doi: 10.1017/S0962492902000016. |
[10] |
M. T. Chu and G. H. Golub, "Inverse Eigenvalue Problems: Theory, Algorithms and Applications,", Oxford University Press, (2005).
doi: 10.1093/acprof:oso/9780198566649.001.0001. |
[11] |
F. Diele, T. Laudadio and N. Mastronardi, On some inverse eigenvalue problems with Toeplitz-related structure,, SIAM J. Matrix Anal. Appl., 26 (2004), 285.
doi: 10.1137/S0895479803430680. |
[12] |
S. Friedland, J. Nocedal and M. L. Overton, The formulation and analysis of numerical methods for inverse eigenvalue problems,, SIAM J. Numer. Anal., 24 (1987), 634.
doi: 10.1137/0724043. |
[13] |
A. Jain, "Fundamentals of Digital Image Processing,", Prentice-Hall, (1989). Google Scholar |
[14] |
E. Montaño, M. Salas and R. L. Soto, Nonnegative matrices with prescribed extremal singular values,, Comput. Math. Appl., 56 (2008), 30.
|
[15] |
E. Montaño, M. Salas and R. L. Soto, Positive matrices with prescribed singular values,, Proyecciones, 27 (2008), 289.
|
[16] |
W. P. Shen, C. Li and X. Q. Jin, A Ulm-like method for inverse eigenvalue problems,, Appl. Numer. Math., 61 (2011), 356.
doi: 10.1016/j.apnum.2010.11.001. |
[17] |
J. A. Tropp, I. S. Dhillon and R. W. Heath Jr., Finite-step algorithms for constructing optimal CDMA signature sequences,, IEEE Trans. Inform. Theory, 50 (2004), 2916.
doi: 10.1109/TIT.2004.836698. |
[18] |
S. W. Vong, Z. J. Bai and X. Q. Jin, An Ulm-like method for inverse singular value problems,, SIAM J. Matrix Anal. Appl., 32 (2011), 412.
doi: 10.1137/100815748. |
[19] |
S. F. Xu, "An Introduction to Inverse Eigenvalue Problems,", Peking University Press and Vieweg Publishing, (1998). Google Scholar |
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