Math 170A Assignment # 7 solved

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1. Exercise 3.2.48.
2. Write your own Matlab code to compute QR factorization with:
Input: A matrix A ∈ R
m×n with m ≥ n.
Output: An orthorgonal matrix Q ∈ R
m×m and an upper triangular R ∈ R
m×n
such that
A = QR.
Look at iteration formula in (3.2.43). Test your code on matrices generated by randn(m,n)
in Matlab.
3. Exercise 3.3.10.
4. Write your own Matlab code to implement the Gram-Schmidt process with:
Input: A matrix A ∈ R
m×n with m ≥ n.
Output: An isometric matrix Q ∈ R
m×n and an upper triangular R ∈ R
n×n
, such that
A = QR and the diagonal entries of R are nonnegative.
Look at iteration formula in (3.4.19). Test your code on matrices generated by randn(m,n)
in Matlab.
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