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Unit 10.1.2 Overview

  • 10.1 Opening Remarks

    • 10.1.1 Subspace iteration with a Hermitian matrix

    • 10.1.2 Overview

    • 10.1.3 What you will learn

  • 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

  • 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

  • 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)

  • 10.5 Wrap Up

    • 10.5.1 Additional homework

    • 10.5.2 Summary