NAG Fortran Library Routine Document C02AGF
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چکیده
The routine generates a sequence of iterates z1; z2; z3; . . ., such that jP ðzkþ1Þj < jP ðzkÞj and ensures that zkþ1 þ Lðzkþ1Þ ‘roughly’ lies inside a circular region of radius jF j about zk known to contain a zero of P ðzÞ; that is, jLðzkþ1Þj jF j, where F denotes the Féjer bound (see Marden (1966)) at the point zk. Following Smith (1967), F is taken to be minðB; 1:445nRÞ, where B is an upper bound for the magnitude of the smallest zero given by
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Note: this routine uses optional parameters to define choices in the problem specification and in the details of the algorithm. If you wish to use default settings for all of the optional parameters, you need only read Section 1 to Section 9 of this document. Refer to the additional Section 10, Section 11 and Section 12 for a detailed description of the algorithm, the specification of the optio...
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where Ni x ð Þ denotes the normalized cubic B-spline defined upon the knots i; iþ1; . . . ; iþ4. The total number n of these knots and their values 1; . . . ; n are chosen automatically by the routine. The knots 5; . . . ; n 4 are the interior knots; they divide the approximation interval x1; xm 1⁄2 into n 7 subintervals. The coefficients c1; c2; . . . ; cn 4 are then determined as the solution...
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