Vector Continued Fractions using a Generalised Inverse

Details Vector Continued Fractions using a Generalised Inverse Vector Continued Fractions using a Generalised Inverse

2003-10-21

arxiv.org/abs/math-ph/0310041v2

J. Phys. A: Mathematical and General, Vol. 37, pages 161-72 (2004)

Physics

Mathematical Physics

Published form - minor changes

Scientific paper

10.1088/0305-4470/37/1/011

A real vector space combined with an inverse for vectors is sufficient to define a vector continued fraction whose parameters consist of vector shifts and changes of scale. The choice of sign for different components of the vector inverse permits construction of vector analogues of the Jacobi continued fraction. These vector Jacobi fractions are related to vector and scalar-valued polynomial functions of the vectors, which satisfy recurrence relations similar to those of orthogonal polynomials. The vector Jacobi fraction has strong convergence properties which are demonstrated analytically, and illustrated numerically.

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