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In the mathematical field of numerical analysis, discrete spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a discrete spline. A discrete spline is a piecewise polynomial such that its central differences are continuous at the knots whereas a spline is a piecewise polynomial such that its derivatives are continuous at the knots. Discrete cubic splines are discrete splines where the central differences of orders 0, 1, and 2 are required to be continuous. Discrete splines were introduced by Mangasarin and Schumaker in 1971 as solutions of certain minimization problems involving differences. ==Discrete cubic splines== Let ''x''1, ''x''2, . . ., ''x''''n''-1 be an increasing set of real numbers. Let ''g''(''x'') be a piecewise polynomial defined by : where ''g''1(''x''), . . ., ''g''''n''(''x'') are polynomials of degree 3. Let ''h'' > 0. If : then ''g''(''x'') is called a discrete cubic spline.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Discrete spline interpolation」の詳細全文を読む スポンサード リンク
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