ALAFF What you will learn

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Subsection 11.1.3 What you will learn

This week, you finally discover practical algorithms for computing the Signgular Value Decomposition.

Upon completion of this week, you should be able to

Link the (Reduced) SIngular Value Decomposition of \(A \) to the Spectral Decomposition of \(A^H A \text{.}\)
Reduce a matrix to bidiagonal form.
Transform the implicitly shifted QR algorithm into the implicitly shifted bidiagonal QR algorithm.
Use Jacobi rotations to propose alternative algorithms, known as Jacobi's Methods, for computing the Spectral Decomposition of a symmetric matrix and Singular Value Decomposition of a general real-valued matrix.