Using Gram-Schmidt process find a QR factorization of the follo... | Filo
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Using Gram-Schmidt process find a QR factorization of the follo... | Filo
Solution For Using Gram-Schmidt process find a QR factorization of the following matrix⎝⎛ 123 134 257 ⎠⎞
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QR factorization of first i columns of A. Suppose the n×k matr... | Filo
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SOLVED: In this exercise, you will prove stability of QR factorisation. You can hide factors depending on m and n in the stability calculations. Let ε denote the machine precision.- Let x=(x1, …, xm) be a vector and consider the Householder transformation corresponding to it, i.e., let v be the unit vector along x sign(x1)x e1. Suppose we compute a unit vector ṽ instead. Show that ṽ-v=O(ε).- Let x, v, ṽ be as above, and let y be a vector of length m. We would like to compute b=y-2v, but we use ṽ
SOLVED: In this exercise, you will prove stability of QR factorisation. You can hide factors depending on m and n in the stability calculations. Let ε denote the machine precision.- Let x=(x1, …, xm) be a vector and consider the Householder transformation corresponding to it, i.e., let v be the unit vector along x sign(x1)x e1. Suppose we compute a unit vector ṽ instead. Show that ṽ-v=O(ε).- Let x, v, ṽ be as above, and let y be a vector of length m. We would like to compute b=y-2v, but we use ṽ
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