How bad are symmetric Pick matrices

作者: Dario Fasino , Vadim Olshevsky

DOI: 10.1117/12.406491

关键词:

摘要: Let P be a symmetric positive definite Pick matrix of order n. The following facts will proven here: (1) is the Gram set rational functions, with respect to an inner product defined in terms 'generating function' associated P; (2) Its condition number lower-bounded by function growing exponentially (3) can effectively preconditioned generated same nodes and constant function.

参考文章(19)
I. Gohberg, A. E. Frazho, M. A. Kaashoek, C. Foias, Metric Constrained Interpolation, Commutant Lifting and Systems ,(1998)
Israel Gohberg, Leiba Rodman, Joseph A. Ball, Interpolation of Rational Matrix Functions ,(1990)
Thomas Kailath, Ali H. Sayed, Displacement Structure: Theory and Applications SIAM Review. ,vol. 37, pp. 297- 386 ,(1995) , 10.1137/1037082
R. Ackner, T. Kailath, On the Ptak-Young generalization of the Schur-Cohn theorem IEEE Transactions on Automatic Control. ,vol. 37, pp. 1601- 1604 ,(1992) , 10.1109/9.256392
Evgenij E. Tyrtyshnikov, How bad are Hankel matrices Numerische Mathematik. ,vol. 67, pp. 261- 269 ,(1994) , 10.1007/S002110050027
J. M. Taylor, The condition of gram matrices and related problems Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 80, pp. 45- 56 ,(1978) , 10.1017/S030821050001012X
Walter Gautschi, Gabriele Inglese, Lower bounds for the condition number of Vandermonde matrices Numerische Mathematik. ,vol. 52, pp. 241- 250 ,(1987) , 10.1007/BF01398878