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2. On each interval I ]. i-0,..n 1, with length h, the cubic spline is given by Write down the (4n) conditions that determine the nat ural cubic spline and the clamped cubic spline. Recall. on each interval 1.-Fez,+1],に0.- n-1. with length h, the cubic spline is given by The equations which define a cubic spline (using the textbook's notation and that used in dass), that is the coefficients satisfy 41- 3h, and the c, are the solutions of the system Co C1 C2 ho 2(ho+hi) h 2(h+ha) h The terms in double square brackets (first and last line) depend on the type of spline required. For a natural cubic spline the first and last row of the matrix are and 0 1 and those of the right hand side are For a clamped cubic spline those are 2ho ho 0 and those of the right hand side are 呵] and . and

Answer 1

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