对称秩一算法近似对称矩阵序列及其应用
Approximation of sequences of symmetric matrices with the symmetric rank-one algorithm and applications
AI总结：
本文提出使用对称秩一算法近似任意对称可逆矩阵序列，拓展了其在约束测地线计算等应用中的使用范围，并提供数值模拟验证。
摘要：
对称秩一更新方法在优化中因其在拟牛顿算法中的应用而广为人知。特别是Conn、Gould和Toint于1991年证明，该方法产生的矩阵序列近似于被最小化的函数的Hessian。扩展这一想法，我们证明对称秩一更新算法可以用来近似任何对称可逆矩阵序列，从而为更一般的问题，如形状分析成像问题中的约束测地线计算等应用增添了多种用途。我们还为该方法和某些应用提供了数值模拟。
英文摘要：
The symmetric rank-one update method is well-known in optimization for its applications in the quasi-Newton algorithm. In particular, Conn, Gould, and Toint proved in 1991 that the matrix sequence resulting from this method approximates the Hessian of the minimized function. Expanding their idea, we prove that the symmetric rank-one update algorithm can be used to approximate any sequence of symmetric invertible matrices, thereby adding a variety of applications to more general problems, such as the computation of constrained geodesics in shape analysis imaging problems. We also provide numerical simulations for the method and some of these applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
