3. By a hand calculation, compute the natural cubic spline interpolating the data points (-1, 1), (0, 0), and (1,2). Thi

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3 By A Hand Calculation Compute The Natural Cubic Spline Interpolating The Data Points 1 1 0 0 And 1 2 Thi 1 (39.75 KiB) Viewed 12 times

3. By a hand calculation, compute the natural cubic spline interpolating the data points (-1, 1), (0, 0), and (1,2). This involves the determination of 8 coefficients of the cubic spline defined by Sa₁r³+b₁x² +c₁r+d₁, a2x³ + b2x² + c2x + d₂, 0 ≤ x ≤ 1, -1 ≤ x ≤0. S(x) = Find a1, b₁, C₁, di and a2, b2, C2, d2. Note that matching at the middle node quickly reduced the number of unknown coefficients from 8 to 4. Applying the condition that it is a natural cubic spline enables you to eliminate 2 more coefficients while fitting the end points will enable you to find all the coefficients by solving a 2 by 2 system.