NAG Fortran Library Routine Document E02DCF

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 knots 5; . . . ; nx 4 and 5; . . . ; ny 4 are the interior knots; they divide the approximation domain x1; xmx y1; ymy h i into nx 7 ð Þ ny 7 subpanels i; iþ1 1⁄2 j; jþ1 h i , for i 1⁄4 4; 5; . . . ; nx 4, j 1⁄4 4; 5; . . . ; ny 4. Then, much as in the curve case (see E02BEF), the coefficients cij are determined as the solution of the following constrained minimization problem: minimize , ð2Þ subject to the constraint