Recessive solutions of block tridiagonal nonhomogeneous systems

Abstract

Olver has given an elegant construction of recessive solutions of nonhomogeneous scalar three term recurrence relations. We investigate the feasibility of applying his methods to block tridiagonal nonhomogeneous systems where the coefficient matrices A B C are n × n matrices and Y and D are n × m. Such systems with m = 1 arise in numerical methods for solving partial differential equations [7,11]. Of course, the results obtained are also applicable to the symmetric case with and symmetric Bk . The homogeneous case with m = n arises in matrix continued fractions [4] and the well-studied symmetric homogeneous case is closely realted to discrete Hamiltonian systems and, for m = n, to discrete Riccati equations [2,1,3,5].