Prof. Matthieu Bloch
Monday, October 28, 2024
Every complex matrix
Every matrix
Every hermitian matrix is unitarily similar to a real-valued diagonal matrix.
Let
We say that
We can write
The solution of
We can separate the error analysis into two components
We will express the error in terms of the SVD
The null space error is given by
The noise error is given by
How do we mitigate the effect of small singular values in
reconstruction?
Truncate the SVD to
Reconstruct
Regularization means changing the problem to solve
The solution is
We have seen several solutions to systems of linear equations
Extension: constrained
least-squares
All these problems involve a symmetric positive definite system of equations.