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ction W, then {po, P₁, Pn} is a linearly independent set. for Chebyshev polynomials 0, n‡m, (Tn, Tm) = π, n = m = 0,

ction W, then {po, P₁, Pn} is a linearly independent set. for Chebyshev polynomials 0, n‡m, (Tn, Tm) = π, n = m = 0,

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 17EQ
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shown that 1₂ and norms on R¹ are equivalent with respect to convergence and show that the sequence x₁ = (2,2, e-2k cos k)* converges to x = (2,0,0) with respect to the 12 norm. Find the least squares polynomials of degrees 1, 2 for the data in the following table Xi yi 1.0 1.9 2.1 1.1 1.3 1.5 1.84 1.96 2.21 2.45 2.94 3.18 Construct orthogonal polynomials {0, 4₁, 42, 4₁} on [0,1] with respect to a weight function w(x)=1 Gram-Schmidt process Show that if {90, 9₁,.., n} is an orthogonal set of functions on [a, b] with respect to the weight function W, then {po, 9₁,.., Pn} is a linearly independent set. Show that for Chebyshev polynomials 0, n‡m, (Tn, Tm) = π, n = m = = 0, 7, n = m = 0.
Transcribed Image Text:shown that 1₂ and norms on R¹ are equivalent with respect to convergence and show that the sequence x₁ = (2,2, e-2k cos k)* converges to x = (2,0,0) with respect to the 12 norm. Find the least squares polynomials of degrees 1, 2 for the data in the following table Xi yi 1.0 1.9 2.1 1.1 1.3 1.5 1.84 1.96 2.21 2.45 2.94 3.18 Construct orthogonal polynomials {0, 4₁, 42, 4₁} on [0,1] with respect to a weight function w(x)=1 Gram-Schmidt process Show that if {90, 9₁,.., n} is an orthogonal set of functions on [a, b] with respect to the weight function W, then {po, 9₁,.., Pn} is a linearly independent set. Show that for Chebyshev polynomials 0, n‡m, (Tn, Tm) = π, n = m = = 0, 7, n = m = 0.
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