AI 中文总结
本文推导了带块三角预条件子的预条件对称多重鞍点矩阵的特征值界，证明非零虚部复特征值的分布范围，且数值结果验证该界能准确描述预条件矩阵的特征值分布。
AI 中文摘要
针对基于近似舒尔补预条件的对称块三对角多重鞍点线性系统，本文推导其特征值界。无论块的数量多少，证明所有具有非零虚部的复特征值严格包含在复平面上以1为中心的圆内；实正特征值则由一系列参数多项式的极值根界定。数值结果表明，该界能很好地刻画预条件矩阵的特征值分布。
英文摘要
We develop eigenvalue bounds for symmetric, block-tridiagonal multiple saddle-point linear systems, preconditioned with block-triangular matrices, based on approximate Schur complements. Irrespective on the number of blocks, we prove that all complex eigenvalues, with nontrivial imaginary part, are strictly contained in a circle within the complex plane, with center 1. The real and positive eigenvalues are bounded in terms of the extremal roots of a sequences of parametric polynomials. Numerical results reveal that the bounds describe very well the eigenvalue distribution of the preconditioned matrix.
