On Applications of the Generalized Fourier Transform in Numerical Linear Algebra

  title={On Applications of the Generalized Fourier Transform in Numerical Linear Algebra},
  author={Krister {\AA}hlander},
Matrices equivariant under a group of permutation matrices are considered. Such matrices typically arise in numerical applications where the computational domain exhibits geometrical symmetries. In these cases, group representation theory provides a powerful tool for block diagonalizing the matrix via the Generalized Fourier Transform. This technique yields substantial computational savings in problems such as solving linear systems, computing eigenvalues and computing analytic matrix functions… CONTINUE READING
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