Modulus of smoothness: Difference between revisions

Revision as of 02:00, 28 March 2015

Revision as of 08:19, 8 April 2015

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In [[mathematics]], '''moduli of smoothness''' are used to quantitatively measure smoothness of functions. Moduli of smoothness generalise [[modulus of continuity]] and are used in [[approximation theory]] and [[numerical analysis]] to estimate errors of approximation by [[polynomial]]s and [[spline]]s.

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of a function <math>f\in C[a,b]</math> is the function <math>\omega_n:[0,\infty)\to\mathbb{R}</math> defined by

:<math>\omega_n(t,f,[a,b])=\sup_{h\in[0,t]}\sup_{x\in[a,b-nh]}|\Delta_h^n(f,x)|\text{ for }0\le t\le \frac{b-a} n,</math>

and

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[[Category:Approximation theory]]

[[Category:Numerical analysis]]

[[Category:Numerical analysis]]