Abstract
Recently, the author proposed a new nonlinear sequence transformation, the iterative
J
transformation, which was shown to provide excellent results in several applications (Homeier [15]). In the present contribution, this sequence transformation is derived by a hierarchically consistent iteration of some basic transformation. Hierarchical consistency is proposed as an approach to control the ...
Abstract
Recently, the author proposed a new nonlinear sequence transformation, the iterative
J
transformation, which was shown to provide excellent results in several applications (Homeier [15]). In the present contribution, this sequence transformation is derived by a hierarchically consistent iteration of some basic transformation. Hierarchical consistency is proposed as an approach to control the well-known problem that the basic transformation can be generalized in many ways. Properties of the J transformation are studied. It is of similar generality as the well-known E algorithm (Brezinski [3], Håvie [18]). It is shown that the J transformation can be implemented quite easily. In addition to the defining representation, there are alternative algorithms for its computation based on generalized differences. The kernel of the
J transformation is derived. The expression for the kernel is relatively compact and does not depend on any lower-order transforms. It is shown that several important other sequence transformations can be computed in an economical way using the J transformation.
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