Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares [Bookshelf]
Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares [Bookshelf]
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DOI：
10.1109/mcs.2020.3019153
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发表时间：
2020-12
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影响因子：
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通讯作者：
G. Strang
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文献类型：
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作者：
G. Strang
最小二乘问题本身是一个非常实用的问题，令人满意的几何（投影到子空间）和良好的线性代数的混合体。基本问题是最小化二次成本函数|Ax − B||.几何学是将B投影到A的列空间上。线性代数产生最优解xt的正规方程AAxt = Ab。矩阵AA绝对是所有应用数学的核心，而且很容易思考。然而，有一个问题：AA通常对计算没有吸引力。Boyd和Vandenberghe围绕这个重要问题创建了一个完整的应用线性代数课程。
The least-squares problem presents itself as a neat mixture of extreme practical importance, satisfying geometry (projections onto subspaces), and good linear algebra. The basic problem is to minimize the quadratic cost function |Ax − b||. The geometry is to project b onto the column space of A. Linear algebra produces the normal equations AAxt = Ab for the optimal solution xt. The matrix AA is absolutely central to all of applied mathematics and is beautiful to think about. However, there is a catch: AA is often not attractive to compute with. Boyd and Vandenberghe have created an entire applied linear algebra course around this important problem.