In this talk, we discuss two topics: (1) Fast Fourier Transform (FFT) (2) QR algorithm. The two algorithms will be explained through the viewpoint of matrix decompositions.

Fast Fourier transforms are widely used for applications in engineering, science, and mathematics. It was listed in Top 10 Algorithms of 20th Century by the IEEE journal Computing in Science and Engineering We will give an intuitive explanation of why it becomes fast with some clever manipulations on the discrete Fourier transform.

The QR algorithm is a procedure to calculate the eigenvalues and eigenvectors of a matrix. We will highlight the connection between the power method and the QR algorithm.