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Exercise 6.2.21

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Apply the same method as in Exercise 6.2.19. Let ${u_{1}, u_{2}, u_{3}}$ be the orthonormal basis given by Example 5 of this section. Then the closest second-degree polynomial approximation is the orthogonal projection

⟨ e^{t}, u_{1} ⟩ u_{1} + ⟨ e^{t}, u_{2} ⟩ u_{2} + ⟨ e^{t}, u_{3} ⟩ u_{3}

= \frac{1}{4} [(15 e - 105 e^{- 1}) t^{2} + 12 t - 3 e^{2} + 33] .

jephianlin

2011-06-27 00:00

Exercise 6.2.21

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