Subsection 10.1.2 Overview
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10.1 Opening
10.1.1 Subspace iteration with a Hermitian matrix
10.1.2 Overview
10.1.3 What you will learn
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10.2 From Power Method to a simple QR algorithm
10.2.1 A simple QR algorithm
10.2.2 A simple shifted QR algorithm
10.2.3 Deflating the problem
10.2.4 Cost of a simple QR algorithm
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10.3 A Practical Hermitian QR Algorithm
10.3.1 Reducing the cost of the QR algorithm
10.3.2 Reduction to tridiagonal form
10.3.3 Givens' rotations
10.3.4 Simple tridiagonal QR algorithm
10.3.5 The implicit Q theorem
10.3.6 The Francis implicit QR Step
10.3.7 A complete algorithm
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10.4 Enrichments
10.4.1 QR algorithm among the most important algorithms of the 20th century
10.4.2 Who was John Francis
10.4.3 Casting the reduction to tridiagonal form in terms of matrix-matrix multiplication
10.4.4 Optimizing the tridiagonal QR algorithm
10.4.5 The Method of Multiple Relatively Robust Representations (MRRR)
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10.5 Wrap Up
10.5.1 Additional homework
10.5.2 Summary