A tricirculant matrix

is tridiagonal except for its (1. n) and (u. 1) entries. Tricirculant matrices arise in the numerical solution of periodic boundary value problems and in spline interpolation.
(a) Prove that if C = LU is regular, its factors have the form

(b) Compute the LU factorization of the n x n tricirculant matrix

for n = 3. 5 and 6. What goes wrong when n =4?

|q, r1 Pi P2 42 2 P3 933 Pa la-2 1 m-2 -1 m1 m2 m3 m4-2 di u 2 u2 3 43 dn- un-1 1 2-1