与微分方程特征值的逆问题相比，正在蓬勃发展的矩阵特征值逆问题有更为丰富的理论和更多有效的数值方法。因此，本项目拟研究Sturm-Liouville特征值逆问题的矩阵方法，即通过求解相应的矩阵特征值逆问题来重构未知系数函数。我们采用最优网格、特征值修正和函数插值等方法，缩小Sturm-Liouville 特征值的逆问题与其逼近问题的误差，再结合矩阵特征值逆问题的理论与算法、多重网格思想和灵敏度分析，设计求解Sturm-Liouville特征值逆问题的有效算法并给出收敛性分析和数值算例。本项目的预期成果不仅能丰富逆谱问题的收敛理论，相关算法也能服务于故障诊断和安全检测,具有重要的理论意义和实用价值。

Since, compared with the inverse eigenvalue problem of differential equation, the matrix inverse eigenvalue problems have much more abundant theory and much more efficient numerical methods, this project is concerned with matrix methods for inverse Sturm-Liouville problems. It is to recover the unknown coefficient by solving a related matrix inverse eigenvalue problem. First, the discrepancy between the inverse Sturm-Liouville problem and the approximation problem is reduced by using optimal grids, correction, interpolation methods and so on. Then based on the results of matrix inverse eigenvalue problem, multigrids and sensitivity analysis, we design efficient algorithms for inverse Sturm-Liouville problem and then establish the convergence and give numerical experimens. The expected results of this project will not only enrich the convergence theories of inverse spectral problem, but also can be used for damage detection and safety inspection. So the research has important theoretical significance and practical value.