An incomplete tridiagonalization-based determinant evaluation for a generalized periodic tridiagonal matrix

TL;DR: A survey of algorithms for solving the eigenproblem for a class of matrices of nearly tridiagonal form that arise from eigenvalue problems for differentia1 equations where the solution is subject to periodic boundary conditions.

TL;DR: A new breakdown-free recursive algorithm for computing the determinant of the periodic tridiagonal matrix with Toeplitz structure via a three-term recurrence, which theoretically produces exact values for periodictridiagonal matrices whose entries are all given in integer.

TL;DR: A novel symbolic algorithm for solving periodic tridiagonal linear systems without imposing any restrictive conditions is presented and its computational cost is less than or almost equal to those of three well-known algorithms.

TL;DR: A new class of parallel Gaussian elimination algorithms is presented for the solution of tridiagonal matrix systems, called ACER, which combine the advantages of the well known cyclic elimination algorithm and the cyclic reduction algorithms.