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OALib Journal期刊
ISSN: 2333-9721
费用:99美元
投稿
时间不限
( 2673 )
( 2672 )
( 2024 )
( 2023 )
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The approximation evaluations by polynomial splines are well-known. They are obtained by the similarity principle; in the case of non-polynomial splines the implementation of this principle is difficult. Another method for obtaining of the evaluations was discussed earlier (see [1]) in the case of nonpolynomial splines of Lagrange type. The aim of this paper is to obtain the evaluations of approximation by non-polynomial splines of Hermite type. Considering a linearly independent system of column-vectors, . Let be square matrix. Supposing that and are columns with components from the linear space such that . Let be vector with components belonging to conjugate space . For an element we consider a linear combination of elements By definition, put . The discussions are based on the next assertion. The following relation holds: where the second factor on the right-hand side is the determinant of a block-matrix of order m + 2. Using this assertion, we get the representation of residual of approximation by minimal splines of Hermite type. Taking into account the representation,