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Q3. Prove that if g interpolates the function f at ro, T1, . .. , In-1 and if h interpolates f at X1,..., Xn, then the function xo - x F(x) = g(x) + In (g(x) – h(x)) - TO interpolates f at xo,..., Tn. Notice that h and g need not be polynomials.

Q3. Prove that if g interpolates the function f at ro, T1, . .. , In-1 and if h interpolates f at X1,..., Xn, then the function xo - x F(x) = g(x) + In (g(x) – h(x)) - TO interpolates f at xo,..., Tn. Notice that h and g need not be polynomials.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q3. Prove that if g interpolates the function f at r0, T1,. .. , Tn-1 and if h interpolates f at X1, ... , Tn, then the function xo - x F(x) = g(x) + In (g(x) – h(x)) - I0 interpolates f at ro,... , Xn. Notice that h and g need not be polynomials.
Transcribed Image Text:Q3. Prove that if g interpolates the function f at r0, T1,. .. , Tn-1 and if h interpolates f at X1, ... , Tn, then the function xo - x F(x) = g(x) + In (g(x) – h(x)) - I0 interpolates f at ro,... , Xn. Notice that h and g need not be polynomials.
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