论文标题
完全不确定的stieltjes力矩问题和padé近似值
Full indefinite Stieltjes moment problem and Padé approximants
论文作者
论文摘要
通过分步Schur算法研究了完整的无限性矩阵问题。自然与不确定的stieltjes力矩问题相关的是普遍的stieltjes持续分数和一个差异方程系统，这反过来导致不确定的stieltjes瞬间问题的分解矩阵分解。在不确定的情况下，发现了这种问题不确定的标准不确定，并且对其解决方案进行了完整描述。提出了对对角线和亚对角线帕德板的显式公式，用于对应于不确定的stieltjes力矩问题的正式功率序列和padé近似值的收敛结果。
Full indefinite Stieltjes moment problem is studied via the step-by-step Schur algorithm. Naturally associated with indefinite Stieltjes moment problem are generalized Stieltjes continued fraction and a system of difference equations, which, in turn, lead to factorization of resolvent matrices of indefinite Stieltjes moment problem. A criterion for such a problem to be indeterminate in terms of continued fraction is found and a complete description of its solutions is given in the indeterminate case. Explicit formulae for diagonal and sub-diagonal Padé approximants for formal power series corresponding to indefinite Stieltjes moment problem and convergence results for Padé approximants are presented.
