Toeplitz matrices: multiply a Toeplitz matrix by a vector using FFT.
Analyze the toeplitz matrices: multiply a toeplitz matrix by a vector using fft..
Examples
Input:"test_input_1"
Output:"output_1"
Input:"test_input_2"
Output:"output_2"
Hints
Recall that a Toeplitz matrix has constant diagonals, meaning each descending diagonal from left to right is constant. How can this property be leveraged to represent the matrix efficiently?
Consider the circulant matrix, a special case of Toeplitz matrices. How does the multiplication of a circulant matrix with a vector relate to the Discrete Fourier Transform (DFT)?
Extend the circulant matrix concept to general Toeplitz matrices. How can the multiplication of a Toeplitz matrix with a vector be decomposed into operations involving circulant matrices and the Fast Fourier Transform (FFT)?
Toeplitz matrices: multiply a Toeplitz matrix by a vector using FFT.
Analyze the toeplitz matrices: multiply a toeplitz matrix by a vector using fft..