The objective of this note is to approximate a birth and death matrix B by a close Toeplitz-type one for which explicit formulas for the eigenpairs are known. Numerical evidence of the approximation behavior of the eigenvalues and eigenvectors of B by those of such Toeplitz-type matrices is provided.

中文翻译：

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逼近出生和死亡矩阵的特征值和特征向量

本注释的目的是通过一个接近的Toeplitz类型的出生和死亡矩阵B进行近似，对于该矩阵已知本征对的明确公式。提供了通过此类Toeplitz型矩阵对B的特征值和特征向量的近似行为的数值证据。