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Consider a set of four data points: f(0) = 3, f(4) = -2, f(-1) = 2, and f(1) = 1. In the following, use these data points to find the best fit polynomial of degree 2 by using the QR-decomposition method: (a) Identify the matrix A and b. Now, write down the linearly independent column vectors u₁, u₂ and u3 from the matrix A. (b) Using the Gram-Schmidt process construct the orthonormal column matrices (or vectors) q1, 92 and q3 from the linearly independent column vectors obtained in the previous part, and then write down the Q matrix. (c) Now calculate the matrix elements of R, and write down the matrix R.

Consider a set of four data points: f(0) = 3, f(4) = -2, f(-1) = 2, and f(1) = 1. In the following, use these data points to find the best fit polynomial of degree 2 by using the QR-decomposition method: (a) Identify the matrix A and b. Now, write down the linearly independent column vectors u₁, u₂ and u3 from the matrix A. (b) Using the Gram-Schmidt process construct the orthonormal column matrices (or vectors) q1, 92 and q3 from the linearly independent column vectors obtained in the previous part, and then write down the Q matrix. (c) Now calculate the matrix elements of R, and write down the matrix R.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
Problem 16EQ
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1. Consider a set of four data points: f(0) = 3, ƒ(4) = -2, f(-1) = 2, and f(1) = 1. In the following, use these data points to find the best fit polynomial of degree 2 by using the QR-decomposition method: Identify the matrix A and b. Now, write down the linearly independent column vectors u₁, u2 and uz from the matrix A. (b) Using the Gram-Schmidt process construct the orthonormal column matrices (or vectors) 91, 92 and q3from the linearly independent column vectors obtained in the previous part, and then write down the Q matrix. (c) Now calculate the matrix elements of R, and write down the matrix R.
Transcribed Image Text:1. Consider a set of four data points: f(0) = 3, ƒ(4) = -2, f(-1) = 2, and f(1) = 1. In the following, use these data points to find the best fit polynomial of degree 2 by using the QR-decomposition method: Identify the matrix A and b. Now, write down the linearly independent column vectors u₁, u2 and uz from the matrix A. (b) Using the Gram-Schmidt process construct the orthonormal column matrices (or vectors) 91, 92 and q3from the linearly independent column vectors obtained in the previous part, and then write down the Q matrix. (c) Now calculate the matrix elements of R, and write down the matrix R.
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