NAG Fortran Library Routine Document E02BEF
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چکیده
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 of the following constrained minimization problem: minimize
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NAG Fortran Library Routine Document E02DDF
where MiðxÞ and NjðyÞ denote normalised cubic B-splines, the former defined on the knots i to iþ4 and the latter on the knots j to jþ4. For further details, see Hayes and Halliday (1974) for bicubic splines and de Boor (1972) for normalised B-splines. The total numbers nx and ny of these knots and their values 1; . . . ; nx and 1; . . . ; ny are chosen automatically by the routine. The knots 5;...
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where Mi x ð Þ and Nj y ð Þ denote normalized cubic B-splines, the former defined on the knots i to iþ4 and the latter on the knots j to jþ4. For further details, see Hayes and Halliday (1974) for bicubic splines and De Boor (1972) for normalized B-splines. The total numbers nx and ny of these knots and their values 1; . . . ; nx and 1; . . . ; ny are chosen automatically by the routine. The kn...
متن کاملNAG Fortran Library Routine Document E04MFF=E04MFA
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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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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In order to define the full set of B-splines required, eight additional knots 1; 2; 3; 4 and nþ4; nþ5; nþ6; nþ7 are inserted automatically by the routine. The first four of these are set equal to the smallest xr and the last four to the largest xr. The representation of sðxÞ in terms of B-splines is the most compact form possible in that only nþ 3 coefficients, in addition to the nþ 7 knots, fu...
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