a.k. from thus spake a.k.
Over the last few months we have seen how we can efficiently implement the Householder transformations and shifted Givens rotations used by Francis's algorithm to diagonalise a real symmetric matrix M, yielding its eigensystem in a matrix V whose columns are its eigenvectors and a diagonal matrix Λ whose diagonal elements are their associated eigenvalues, which satisfy
M = V × Λ × VT
and together are known as the spectral decomposition of M.
In this post, we shall add it to the
and together are known as the spectral decomposition of M.
In this post, we shall add it to the
ak
library using the householder
and givens
functions that we have put so much effort into optimising.