The exponent of convergence for 2-dimensional jacobi-perron type algorithms is studied. By a new formalism, it is shown that the exponent is strictly greater than 1 almost everywhere for the algorithms considered.
The exponent of convergence for 2-dimensional jacobi-perron type algorithms is studied. By a new formalism, it is shown that the exponent is strictly greater than 1 almost everywhere for the algorithms considered.
We study the operator moment problem for a (p + 2)-diagonal nonsymmetric matrix operator and give an explicit form of the Favard theorem for vector orthogonal polynomials. As a main tool we use the development of a sy...
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We study the operator moment problem for a (p + 2)-diagonal nonsymmetric matrix operator and give an explicit form of the Favard theorem for vector orthogonal polynomials. As a main tool we use the development of a system of resolvent functions of the operator in a vector continued fraction by a modified jacobi-perron algorithm.
Abstract: We present an alternative expression of the jacobi-perron algorithm on a set of $n - 1$ independent numbers of an algebraic number field of degree n, where computation of real valued (nonrational) nu...
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Abstract: We present an alternative expression of the jacobi-perron algorithm on a set of $n - 1$ independent numbers of an algebraic number field of degree n, where computation of real valued (nonrational) numbers is avoided. In some instances this saves the need to compute with high levels of precision. We also demonstrate a necessary and sufficient condition for the algorithm to cycle. The paper is accompanied by several numerical examples.
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