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- W2014897584 abstract "By exploiting an isomorphism between vectors and certain matrices, the theory of vector-valued continued fractions is developed as a special case of the theory of matrix-valued continued fractions. It is shown that if a given power series has coefficient vectors lying in Hilbert space, then the vector-valued Padé quotients derived from this series also lie in Hilbert space. Properties of the matrices occuring in the vector-matrix isomorphism are examined; in particular, it is shown that the numerical values of certain norms of a vector are equal to those of the corresponding norms of its companion matrix. The concept of a functional Padé table is introduced, and one of its properties is derived." @default.
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- W2014897584 date "1968-07-01" @default.
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- W2014897584 title "Vector continued fractions" @default.
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- W2014897584 doi "https://doi.org/10.1016/0024-3795(68)90015-3" @default.
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