An Optimal Interpolation Formulas with Derivative in the Space ????(2,1)2
Keywords:
space ????(2,1) 2 (0, 1, an extremal function, the error functional, optimal interpolation formulas, conjucate space, the norm of error functionalAbstract
One of the classical problems in computational mathematics is to construct an interpolation formulas from a countable set of data. This paper demonstrates the problem of construction of optimal interpolation formulas with derivative in the space ????(2,1)2 (0, 1). Here the interpolation formula consists of the linear combination of values of the function at nodes and values of the first derivative of that function at the end points of the interval [0, 1]. For any function of the space ????(2,1) 2 (0, 1) the error of the interpolation formulas is estimated by the norm of the error functional in the conjugate space ????(2,1) 2 (0, 1). The norm of the error functional is calculated for constructing optimal interpolation formulas.
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