标题： 关于Sherman-Morrison-Woodbury公式的稳定性的一点注记 显示英文标题

标题： A Note on the Stability of the Sherman-Morrison-Woodbury Formula

摘要： 我们研究了Sherman-Morrison-Woodbury（SMW）恒等式的数值稳定性。 设 $B = A + UV^T$ 并假设 $U$ 和 $V$ 都具有满列秩。 我们探讨了当只能计算近似逆时，SMW 恒等式的误差界。 对于前向误差和后向误差，我们以近似逆的二范数误差为函数给出了上界。 通过数值实验验证，在某些情况下，我们的界值准确捕捉了误差的行为。 显示英文摘要

摘要： We study the numerical stability of the Sherman-Morrison-Woodbury (SMW) identity. Let $B = A + UV^T$ and assume $U$ and $V$ both have full-column rank. We explore error bounds for the SMW identity when we are only able to compute approximate inverses. For both forward and backward errors, we present upper bounds as a function of the two-norm error of the approximate inverses. We verify with numerical experiments that, in certain cases, our bounds accurately capture the behavior of the errors.