準安定な補間過程の一構成法 : 選点補間多項式による函数の逐次近似

概要

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In a successive approximation for a given function f(x) over a finite range by a sequence of interpolating polynomials, we consider on the propagation of rounding error and on the reduction of number of operations.Propagation error may depent upon the norm ‖L_n‖ of n-1th interpolating polynomial L_n(f;x). If the norm ‖L_n‖ satisfies lim__<n→∞>‖L_n‖=∞ and lim__<n→∞>‖L_n‖^<1/n>=1, then we call in this paper the interpolation semi-stable. We construct a semi-stable and "economical" interpolation process generating the interpolating points by a simple algorithm. As the application,we show two methods to obtain the truncated series of Chebyshev or Legendre polynomials for a "well-behaved" function on [-1,1] without their zero point.
一般社団法人情報処理学会の論文
1968-07-15