VECTOR AND MATRIX SEQUENCE TRANSFORMATIONS BASED ON BIORTHOGONALITY

Sequence transformations are used for the purpose of convergence accel eration. An important algebraic property connected with a sequence tra nsformation is its kernel, that is the set of sequences transformed in to a constant sequence (usually the limit of the sequence). In this pa per, we show how to construct transformations whose kernels are the se ts of vector or matrix sequences of the forms x(n) = x + Z(n) alpha, x (n) = x + Z(n) alpha(n) and x(n) = x + Z(n) alpha(n) + Y-n beta where Z(n) and Y-n are known matrices, alpha, alpha(n) and beta unknown vect ors or matrices. Recursive algorithms for their implementation are giv en. Applications to the solution of systems of linear and nonlinear eq uations are also discussed.