Quadratic pencils and least-squares piecewise-polynomial approximation

Author:
Boris Mityagin

Journal:
Math. Comp. **40** (1983), 283-300

MSC:
Primary 41A15; Secondary 47A68

DOI:
https://doi.org/10.1090/S0025-5718-1983-0679446-0

MathSciNet review:
679446

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Abstract: For a partition of the unit interval, , , denotes the space of piecewise-polynomials of order *k* and of smoothness ; this space can be represented as the graph of the appropriate linear operator between two finite-dimensional Hilbert spaces. It gives an approach to the C. de Boor problem, 1972, on uniform boundedness (with respect to ) in the -norm of the orthogonal projections onto , and we give the detailed analysis of a quadratic pencil (matrix-valued polynomial of the second degree) which appears in the case of a geometric mesh if . The explicit calculations and estimates of zeros of the "characteristic" polynomial show that in the case , me geometric mesh with the parameter *x*, , the orthogonal projectors are uniformly bounded.

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DOI:
https://doi.org/10.1090/S0025-5718-1983-0679446-0

Article copyright:
© Copyright 1983
American Mathematical Society