本文應用無網格法（Meshless method）中的具對稱系統矩陣之局部最小二乘無網格法來分析探討邊界值與特徵值問題。本法主要使用局部最小二乘法(Local least-square method, LLS)建立局部聯立方程組並使其對稱化，再加總為全域聯立方程組，本文稱其為對稱化局部最小二乘法(Symmetrize local least-square method, SLLS)
　　本文中數值範例所得結果和解析解進行比較，在邊界值問題的收斂性與精度都明顯較舊有的數值方法更令人滿意而在特徵值問題上大大減少許多雜亂與錯誤的特徵值訊息，因此驗證了具對稱微分矩陣之局部最小二乘無網格法在邊界值與特徵值問題上的可行性。

In this paper we introduce the meshless method of local least-square with symmetric system matrix to solve the boundary value problem and eigenvalue problems. We use the local least-square method(LLS) to establish a system of equations and improve it to be symmetrical,then combine the local system of equations to a global system of equation. In this paper we named the new method Symmetrize local least-square method, SLLS .

　　In the numerical example we comparing the data analyzed in this article with the exact solution, It shows that SLLS have good convergency and accuracy to be used on the boundary value and eigenvalue problems.

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