MATRIX TRANSFORMS OF λ-BOUNDEDNESS DOMAINS OF THE ZWEIER METHOD

MATRIX TRANSFORMS OF λ-BOUNDEDNESS DOMAINS OF THE ZWEIER METHOD

A. Aasma, H. Dutta

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Abstract

In this paper, we nd necessary and sucient conditions for the Zweier matrix method Z1=2 to be transform from the spaces of -bounded and -convergent sequences into the spaces of -bounded and -convergent sequences, where  and  are monotonically increasing sequences with positive entries (i.e. speeds). Also we nd necessary and sucient conditions for a matrix M to be transform from the -boundedness domain of Z1=2 into the -boundedness domain of a triangular matrix method B: In addition, we introduce one class of multiplicative matrices M satisfying these necessary and sucient conditions.

Keywords

Matrix transforms, convergence and boundedness with speed, Zweier method, factorable matrices.