DOMINANT AND RECESSIVE SOLUTIONS OF SYMMETRICAL 3 TERM RECURRENCES

[摘要] Dominant and recessive solutions are defined for matrix three term recurrences -K(n)X(n-1) + B(n)X(n) - K(n-1)T X(n-1) =0. Eventual disconjugacy is shown to imply existence of a recessive solution at infinity and, furthermore, that an associated Riccati equation W(n+1) = A(n) + E(n)-1W(n)(W(n) + C(n-1))-1C(n-1)(E(n)T)-1 has an eventually minimal solution W(n)-. Riccati equations of this form with A(n) and C(n) positive definite arise in the discrete regulator problem. (C) 1994 Academic Press, Inc.

[发布日期] 1994-01-15