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(a) (i) The data below are generated using function f(x) = x cosx-2x² + 3x - 1. Use appropriate Lagrange interpolating formula to approximate f(0.25). 0.0 0.1 0.2 0.3 x f(x) -1.0 0.4 -0.62049958 -0.28398668 0.00660095 0.24842440 1 (ii) Use Lagrange error formula to find a bound for the error and compare the bound to the actual error. (b) Approximate F(0.05) using the following data and Newton's forward- difference formula,

(a) (i) The data below are generated using function f(x) = x cosx-2x² + 3x - 1. Use appropriate Lagrange interpolating formula to approximate f(0.25). 0.0 0.1 0.2 0.3 x f(x) -1.0 0.4 -0.62049958 -0.28398668 0.00660095 0.24842440 1 (ii) Use Lagrange error formula to find a bound for the error and compare the bound to the actual error. (b) Approximate F(0.05) using the following data and Newton's forward- difference formula,

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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Question 2 (a) (i) The data below are generated using function f(x) = x cosx-2x² + 3x - 1. Use appropriate Lagrange interpolating formula to approximate f(0.25). 0.0 0.2 0.3 -1.0 x f(x) 0.1 -0.62049958 -0.28398668 0.00660095 0.24842440 1 x f(x) (ii) Use Lagrange error formula to find a bound for the error and compare the bound to the actual error. (b) Approximate F(0.05) using the following data and Newton's forward- difference formula, 0.4 n Pn = Σ Σ (1) Δ r=0 A' f(xo), s = x-xo h Use 6 significant figures throughout your computations. 0.2 0.4 0.6 0.8 0.0 1.00000 1.22140 1.49182 1.82212 2.22554
Transcribed Image Text:Question 2 (a) (i) The data below are generated using function f(x) = x cosx-2x² + 3x - 1. Use appropriate Lagrange interpolating formula to approximate f(0.25). 0.0 0.2 0.3 -1.0 x f(x) 0.1 -0.62049958 -0.28398668 0.00660095 0.24842440 1 x f(x) (ii) Use Lagrange error formula to find a bound for the error and compare the bound to the actual error. (b) Approximate F(0.05) using the following data and Newton's forward- difference formula, 0.4 n Pn = Σ Σ (1) Δ r=0 A' f(xo), s = x-xo h Use 6 significant figures throughout your computations. 0.2 0.4 0.6 0.8 0.0 1.00000 1.22140 1.49182 1.82212 2.22554
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