Given the data points (X_1 Y_1) (i = 1, .. ., n + 1), the zeroth order divided d

Question

Given the data points (X_1 Y_1) (i = 1, .. ., n + 1), the zeroth order divided differences are defined by f[x_1] = Y_1. Further, (k - 1)-th order divided differences. (lest hand side below) are given in terms of the (k - 2)-th order divided differences (right hand side) by the recursive formula. For example, for four data points (X_1, Y_1), (X_2, Y_2), (X_3, Y_3) and (X_4, Y_4) difference (DD's) can be listed in a table as shown: Give the expression of the three first order divided differences in terms of the zeroth order DD's Give the expression of the two second order divided differences in terms of the first order DD's Give the expression of the third order divided differences (only one) in terms of the second order DD's

Explanation / Answer

(a)

f[X1, X2] = (f[X2]-f[X1])/(x2-x1)

f[X2, X3] = (f[X3] - f[X2])/(X3-X2)

f[X3, X4] = (f[X4] - f[X3])/(X4-X3)

(b)

f[X1, X2, X3] = (f[X2, X3] - f[X1, X2])/(X3-X1)

f[X2, X3, X4] = (f[X3, X4] - f[X2, X3])/(X4-X2)

(c)

f[X1, X2, X3, X4] = (f[X2, X3, X4] - f[X1, X2, X3])/(X4-X1)

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.