Constructing symmetric nonnegative matrices via the fast fourier transform

✍ Scribed by O. Rojo; H. Rojo

• Book ID: 104352513
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 1021 KB
• Volume: 45
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(03)00145-7

✦ Synopsis

derive an algorithm based on the fast Fourier transform to construct a real symmetric matrix S with eigenvalues Xl 2 x2 2 '. 2 A,, with eigenvector e = [l, 1,. . . , llT belonging to the eigenvalue Xl. We find simple conditions on the eigenvalues such that the algorithm constructs an irreducible matrix S = XlE, where E is a symmetric doubly stochastic matrix.