Deviation of an approximating function

The distance between the approximating function and a given function . In one and the same class different metrics may be considered, e.g. the uniform metric

an integral metric

and other metrics. As the class of approximating functions one may consider algebraic polynomials, trigonometric polynomials and also partial sums of orthogonal expansions of in an orthogonal system, linear averages of these partial sums as well as a number of other sets.

References

[1]	P.L. Chebyshev, "Complete collected works" , 2 , Moscow-Leningrad (1947) (In Russian)
[2]	I.P. Natanson, "Constructive function theory" , 1–3 , F. Ungar (1964–1965) (Translated from Russian)
[3]	V.L. Goncharov, "The theory of interpolation and approximation of functions" , Moscow (1954) (In Russian)
[4]	N.I. [N.I. Akhiezer] Achiezer, "Theory of approximation" , F. Ungar (1956) (Translated from Russian)
[5]	S.M. Nikol'skii, "Approximation of functions of several variables and imbedding theorems" , Springer (1975) (Translated from Russian)

References

[a1]	E.W. Cheney, "Introduction to approximation theory" , Chelsea, reprint (1982)
[a2]	A. Schönhage, "Approximationstheorie" , de Gruyter (1971)