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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Quadratic pencils and least-squares piecewise-polynomial approximation
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by Boris Mityagin PDF
Math. Comp. 40 (1983), 283-300 Request permission


For a partition $\xi = (0 = {\xi _0} < {\xi _1} < \cdots < {\xi _n} < {\xi _{n + 1}} = 1)$ of the unit interval, $S_\xi ^{km}$, $k > m$, denotes the space of piecewise-polynomials of order k and of smoothness $m - 1$; 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 $\xi$) in the ${L_\infty }$-norm of the orthogonal projections onto $S_\xi ^{km}$, 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 $\xi$ if $2m \leqslant k$. The explicit calculations and estimates of zeros of the "characteristic" polynomial show that in the case $S_{\xi (x)}^{63}$, $\xi (x)$ me geometric mesh with the parameter x, $0 < x < \infty$, the orthogonal projectors are uniformly bounded.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Math. Comp. 40 (1983), 283-300
  • MSC: Primary 41A15; Secondary 47A68
  • DOI:
  • MathSciNet review: 679446