On bounding for banded
Author:
Stephen Demko
Journal:
Math. Comp. 33 (1979), 12831288
MSC:
Primary 65F35; Secondary 41A15
MathSciNet review:
537972
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Abstract: Upper bounds for in terms of inverses of certain submatrices are obtained for band matrices. An application to a problem in spline theory is made.
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 [1]
 C. DE BOOR, "Bounding the error in spline interpolation," SIAM Rev., v. 16, 1974, pp. 531544. MR 0361531 (50:13976)
 [2]
 C. DE BOOR, "On the convergence of odddegree spline interpolation," J. Approximation Theory, v. 1, 1968, pp. 452463. MR 0237996 (38:6273)
 [3]
 C. DE BOOR, "On bounding spline interpolation," J. Approximation Theory, v. 14, 1975, pp. 191203. MR 0382911 (52:3793)
 [4]
 C. DE BOOR, OddDegree Spline Interpolation at a BiInfinite Knot Sequence, MRC TSR #1666, August, 1976.
 [5]
 C. DE BOOR, "A bound on the norm of the approximation by splines in terms of a global mesh ratio," Math. Comp., v. 30, 1976, pp. 765771. MR 0425432 (54:13387)
 [6]
 S. DEMKO, "Local approximation properties of spline projections," J. Approximation Theory, v. 19, 1977, pp. 176185. MR 0435663 (55:8621)
 [7]
 S. DEMKO, "Inverses of band matrices and local convergence of spline projections," SIAM J. Numer. Anal., v. 14, 1977, pp. 616619. MR 0455281 (56:13520)
 [8]
 J. DOUGLAS, JR., T. DUPONT & L. WAHLBIN, "Optimal error estimates for Galerkin approximations to solutions of twopoint boundary value problems," Math. Comp., v. 29, 1975, pp. 475483. MR 0371077 (51:7298)
 [9]
 R. S. VARGA, "On diagonal dominance arguments for bounding " Linear Algebra and Appl., v. 14, 1976, pp. 211217. MR 0447297 (56:5612)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197905379728
PII:
S 00255718(1979)05379728
Article copyright:
© Copyright 1979
American Mathematical Society
