A bound for the inverse of a lower triangular Toeplitz matrix

SIAM Journal on Matrix Analysis and Applications

Volumn 24, Issue 4, 2003, Pages 1167-1174

  Vecchio, Antonia ^a  

^a CNR   (Italy)

Author keywords

Inverse matrix; Recurrence formula; Toeplitz matrix

Indexed keywords

EID: 0142138707     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479801396762     Document Type: Article

References (20)

1. A. BÖTTCHER AND S. GRUDSKY, Toeplitz Matrices, Asymptotic Linear Algebra and Functional Analysis, Birkhäuser, Basel, 2000.
2. A. BÖTTCHER AND B. SILBERMANN, Introduction to Large Truncated Toeplitz Matrices, Springer, New York, 1999.
3. H. BRUNNER, M. R. CRISCI, V. B. E. RUSSO, AND A. VECCHIO, A family of methods for Abel integral equations of the second order, J. Comput. Appl. Math., 34 (1991), pp. 211-219.
4. H. BRUNNER AND P. J. VAN DER HOUWEN, The Numerical Solution of Volterra Equations, CWI Monographs 3, North-Holland, Amsterdam, 1986.
5. M. R. CRISCI, V. B. KOLMANOVSKII, E. RUSSO, AND A. VECCHIO, Stability of discrete Volterra equations of Hammerstein type, J. Differ. Equations Appl., 6 (2000), pp. 127-145.
6. P. P. B. EGGERMONT, A new analysis of the trapezoidal-discretization method for the numerical solution of Abel-type integral equations, J. Integral Equations, 3 (1981), pp. 317-332.
7. S. N. ELAYDI, An Introduction to Difference Equations, Springer, New York, 1996.
8. W. FELLER, An Introduction to Probability Theory and Its Applications, Vol. 1, John Wiley & Sons, New York, 1950.
9. U. GRENANDER AND G. SZEGÖ, Toeplitz Forms and Their Applications, 2nd ed., Chelsea, New York, 1984.
10. G. GRIPPENBERG, S.-O. LONDEN, AND O. STAFFANS, Volterra Integral and Functional Equations, Cambridge University Press, Cambridge, UK, 1990.
11. G. HEINIG AND K. ROST, Algebraic Methods for Toeplitz-like Matrices and Operators, Birkhäuser, Basel, 1984.
12. P. HENRIOI, Applied and Computational Complex Analysis, Vol. 1, John Wiley & Sons, New York, 1974.
13. P. LINZ, Analytical and Numerical Methods for Volterra Equations, SIAM, Philadelphia, 1985.
14. CH. LUBICH, On the stability of linear multistep methods for Volterra convolution equations, IMA J. Numer. Anal., 3 (1983), pp. 439-465.
15. M. MENEGUITTE, A note on bordered isoclinal matrices, J. Comput. Appl. Math., 17 (1987), pp. 375-377.
16. A. VECCHIO, Stability results on some direct quadrature methods for Volterra integro-differential equations, Dynam. Systems Appl., 7 (1998), pp. 501-518.
17. A. VECCHIO, On the resolvent kernel of Volterra discrete equations, Funct. Differ. Equations, 6 (1999), pp. 191-201.
18. A. VECCHIO, Stability of backward differentiation formulas for Volterra integro-differential equations, J. Comput. Appl. Math., 115 (2000), pp. 565-576.
19. A. VECCHIO, Stability of some linear and nonlinear methods for Volterra integral equations, J. Integral Equations Appl., 12 (2000), pp. 449-465.
20. A. VECCHIO, Volterra discrete equations: Summability of the fundamental matrix, Numer. Math., 89 (2001), pp. 783-794.