Doolittle Factorization is a method used to decompose a square matrix
Therefore, if we need to solve the linear system
Cholesky Factorization is a method used to decompose a Hermitian, positive-definite matrix
A circulant matrix
The linear system
- Apply the DFT to the first column of
$C$ to obtain diagonal matrix$D$ . - Apply the DFT to the right-hand side vector
$b$ , then divide the result elementwise by the diagonal elements of$D$ . - Apply the inverse DFT to the resulting vector.
This efficient algorithm of the circulant matrix system requires only