給定一個對稱矩陣，我們在這篇論文中想要用兩種結構來近似這個對稱矩陣。第一種是對角元素與原始對稱矩陣相同的半正定矩陣，另一種是從原始矩陣的非對角線元素中固定特定位置的相關矩陣。我們的方法是將原始近似問題轉化為無約束的連續可微凸優化問題，並且數值結果也顯示出了這個方法的可行性及效率。

Given a symmetric matrix, we in this work would like to approximate this symmetric matrix with two kinds of structure, i.e., a positive semidefinite matrix with fixed diagonal entries selected from the original symmetric matrix and a correlation matrix with fixed elements outside the diagonal entries. Our approach is to transform the original approximate problem into an unconstrained continuously differentiable convex optimization problem. Numerical experiments seem to suggest the efficiency and effectiveness of our method.

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