On stable calculation of linear functionals
Author:
SvenAke Gustafson
Journal:
Math. Comp. 33 (1979), 694704
MSC:
Primary 65J05; Secondary 65D30
MathSciNet review:
521283
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Abstract: In this paper we discuss the recurrent task of evaluating a linear functional defined by (generally infinitely many) linear constraints. We develop a theory for the stability of this problem and suggest a regularization procedure, based on orthogonal expansions. Simple and efficient computational schemes for evaluating the functional numerically are given.
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 G. DAHLQUIST, Å. BJÖRCK & N. ANDERSON, Numerical Methods, PrenticeHall, Englewood Cliffs, N. J., 1974. MR 0368379 (51:4620)
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 S.ÅA. GUSTAFSON, "Some optimization problems in numerical analysis," Methods of Operations Research, v. 25, 1977, pp. 367379.
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 S.Å. GUSTAFSON, "Convergence acceleration on a general class of power series," Computing, v. 21, 1978, pp. 367379. MR 619912 (83m:65005)
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 S.Å. GUSTAFSON & K. O. KORTANEK, "Numerical treatment of a class of semiinfinite programming problems," Naval Res. Logist. Quart., v. 20, 1973, pp. 477504. MR 0329257 (48:7599)
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 M. J. D. POWELL, "On the maximum norm of polynomial approximation defined by interpolation and by least squares criteria," Comput. J., v. 9, 1967, pp. 404407. MR 0208807 (34:8616)
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 T. RIVLIN, The Chebyshev polynomials, Wiley, New York, 1974. MR 0450850 (56:9142)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197905212830
PII:
S 00255718(1979)05212830
Keywords:
Linear functionals,
moment condition,
linear space,
error bound,
duality lemma
Article copyright:
© Copyright 1979 American Mathematical Society
