Why is it useful to introduce shifts in the qr iteration

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1. What are the two main stages of eigensolvers, and what is the main purpose of the first stage?

2. What is the sparsity pattern of the matrix that is obtained when applying an upper Hessen berg reduction procedure to a symmetric matrix? Why?

3. What is the QR iteration, and how is it connected to the QR decomposition?

4. Why is it useful to introduce shifts in the QR iteration?

5. What is bidiagonalization and how is it related to the computation of SVD?

Reference no: EM131252615

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