A1 Let the inner product for polynomial functions on the interval 0 ≤ x ≤ 1 be given by 1 (§,9) = f f(x)9(x)x dx. (a) Applying the Gram-Schmidt method to the sequence of powers 1, x, x2, x³, find the first three members of the orthonormal basis of polynomials. (1)
A1 Let the inner product for polynomial functions on the interval 0 ≤ x ≤ 1 be given by 1 (§,9) = f f(x)9(x)x dx. (a) Applying the Gram-Schmidt method to the sequence of powers 1, x, x2, x³, find the first three members of the orthonormal basis of polynomials. (1)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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![A1 Let the inner product for polynomial functions on the interval 0 ≤ x ≤ 1 be given by
(f,g) = f* f (x)g(x)r
dx.
(1)
(a) Applying the Gram-Schmidt method to the sequence of powers 1, x, x2, x³,...
find the first three members of the orthonormal basis of polynomials.
(b) Find the best in the mean approximation ao + a1x + a2x² of the function √√x in
the norm defined by the inner product (1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69cce4ac-4bf6-4e6b-8636-bf160e045b58%2F2e784798-4d47-43d8-926b-d50b90af93b7%2F9jwl3aq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A1 Let the inner product for polynomial functions on the interval 0 ≤ x ≤ 1 be given by
(f,g) = f* f (x)g(x)r
dx.
(1)
(a) Applying the Gram-Schmidt method to the sequence of powers 1, x, x2, x³,...
find the first three members of the orthonormal basis of polynomials.
(b) Find the best in the mean approximation ao + a1x + a2x² of the function √√x in
the norm defined by the inner product (1).
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