|Consider a set of four data points: f (0) = 0f (2) =¬If(-1)= 2nd f (1) = 2We now find the solution by QRdecomposition method using these four data points by answering the following: Write down the matrix Aand b. Also identify the linearly independent column vectors u1, Uz and z from the matrix A 2. Using the Gram-Schmidt process construct the orthonormal column matrices (or vectors) q1, q2 and q3 from the linearly independent column vectors u1, Uz and uz obtained in the previous part, and then write down the Qmatrix. 3- Now calculate the matrix elements of R and write down the matrix R 4. Compute Rxand Q"b, where = (ao a1 a2)ʻis a column vector with ao, a1 and az are the coefficients of the polynomial p2. 5. Using the above result, find the values of ao, a1 and az; and write the polynomial p2 (x)
|Consider a set of four data points: f (0) = 0f (2) =¬If(-1)= 2nd f (1) = 2We now find the solution by QRdecomposition method using these four data points by answering the following: Write down the matrix Aand b. Also identify the linearly independent column vectors u1, Uz and z from the matrix A 2. Using the Gram-Schmidt process construct the orthonormal column matrices (or vectors) q1, q2 and q3 from the linearly independent column vectors u1, Uz and uz obtained in the previous part, and then write down the Qmatrix. 3- Now calculate the matrix elements of R and write down the matrix R 4. Compute Rxand Q"b, where = (ao a1 a2)ʻis a column vector with ao, a1 and az are the coefficients of the polynomial p2. 5. Using the above result, find the values of ao, a1 and az; and write the polynomial p2 (x)
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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Transcribed Image Text:Consider a set of four data points: f (0) = Of (2) = ¬f (-1) = 2nd f (1) = 2We now find the solution by QRdecomposition
method using these four data points by answering the following:
Write down the matrix Aand b. Also identify the linearly independent column vectors u1, Uz and uz from the matrix A
a Using the Gram-Schmidt process construct the orthonormal column matrices (or vectors) q1, 92 and q3 from the linearly independent
column vectors u1, Uz and uz obtained in the previous part, and then write down the Q matrix.
3.
Now calculate the matrix elements of R and write down the matrix R
4.
ACompute Rxand Q"b, where x = (ao a1 a2)*is a column vector with ao, a1 and a, are the coefficients of the polynomial p2.
5.
Using the above result, find the values of ao, a1 and a2; and write the polynomial P2 (x)
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