@article{CML_2011__3_2_253_0,
author = {Khalil, Houssam and Mourrain, Bernard and Schatzman, Michelle},
title = {Transformation du probl\`eme de r\'esolution de syst\`emes de {Toeplitz} biniveaux \`a un probl\`eme polynomial},
journal = {Confluentes Mathematici},
pages = {253--262},
publisher = {World Scientific Publishing Co Pte Ltd},
volume = {3},
number = {2},
year = {2011},
doi = {10.1142/S1793744211000357},
language = {fr},
url = {http://archive.numdam.org/articles/10.1142/S1793744211000357/}
}
TY - JOUR AU - Khalil, Houssam AU - Mourrain, Bernard AU - Schatzman, Michelle TI - Transformation du problème de résolution de systèmes de Toeplitz biniveaux à un problème polynomial JO - Confluentes Mathematici PY - 2011 SP - 253 EP - 262 VL - 3 IS - 2 PB - World Scientific Publishing Co Pte Ltd UR - http://archive.numdam.org/articles/10.1142/S1793744211000357/ DO - 10.1142/S1793744211000357 LA - fr ID - CML_2011__3_2_253_0 ER -
%0 Journal Article %A Khalil, Houssam %A Mourrain, Bernard %A Schatzman, Michelle %T Transformation du problème de résolution de systèmes de Toeplitz biniveaux à un problème polynomial %J Confluentes Mathematici %D 2011 %P 253-262 %V 3 %N 2 %I World Scientific Publishing Co Pte Ltd %U http://archive.numdam.org/articles/10.1142/S1793744211000357/ %R 10.1142/S1793744211000357 %G fr %F CML_2011__3_2_253_0
Khalil, Houssam; Mourrain, Bernard; Schatzman, Michelle. Transformation du problème de résolution de systèmes de Toeplitz biniveaux à un problème polynomial. Confluentes Mathematici, Tome 3 (2011) no. 2, pp. 253-262. doi : 10.1142/S1793744211000357. http://archive.numdam.org/articles/10.1142/S1793744211000357/
[1] D. Eisenbud, Commutative Algebra, Graduate Texts in Mathematics, Vol. 150 (Springer-Verlag, 1995), with a view toward algebraic geometry.
[2] B. Friedlander, M. Morf, T. Kailath et L. Ljung, New inversion formulas for matrices classified in terms of their distance from Toeplitz matrices, Linear Algebra Appl. 27 (1979) 31–60.
[3] G. Heinig et K. Rost, Algebraic Methods for Toeplitz-like Matrices and Operators, Operator Theory : Advances and Applications, Vol. 13 (Birkhäuser-Verlag, 1984).
[4] T. Kailath, S. Y. Kung et M. Morf, Displacement ranks of matrices and linear equa- tions, J. Math. Anal. Appl. 68 (1979) 395–407.
[5] G. Labahn et T. Shalom, Inversion of Toeplitz matrices with only two standard equa- tions, Linear Algebra Appl. 175 (1992) 143–158.
[6] H. Michael Möller et F. Mora, New constructive methods in classical ideal theory, J. Algebra 100 (1986) 138–178.
[7] B. Mourrain et V. Y. Pan, Multivariate polynomials, duality, and structured matrices, J. Complexity 16 (2000) 110–180, real computation and complexity (Schloss Dagstuhl, 1998).
[8] S. Serra Capizzano et E. Tyrtyshnikov, Any circulant-like preconditioner for multilevel matrices is not superlinear, SIAM J. Matrix Anal. Appl. 21 (1999) 431–439.
[9] H. Khalil, B. Mourrain and M. Schatzman, Toeplitz and Toeplitz-block-Toeplitz matrices and their correlation with syzygies of polynomials, in Matrix Methods : The- ory, Algorithms, Applications, International seminar matrix methods and operator equations (MM&OE), eds. V. Olshevsky and E. Tyrtyshnikov (World Scientific, 2008), pp. 296–312.
[10] D. Noutsos, S. S. Capizzano and P. Vassalos, Matrix algebra preconditioners for mul- tilevel Toeplitz systems do not insure optimal convergence rate, Theor. Comput. Sci. 315 (2004) 557–579.
[11] E. Tyrtyshnikov, Fast algorithms for block Toeplitz matrices, Sov. J. Numer. Math. Model. 1 (1985) 121–139.
[12] M. Van Barel, G. Heinig and P. Kravanja, A stabilized superfast solver for nonsym- metric Toeplitz systems, SIAM J. Matrix Anal. Appl. 23 (2001) 494–510.
Cité par Sources :
