论文标题
如何投射到封闭的仿射子空间和超平面的交点
How to project onto the intersection of a closed affine subspace and a hyperplane
论文作者
论文摘要
让$ a $为封闭的仿射子空间，让$ b $成为希尔伯特空间中的超平面。假设我们分别为我们提供了相关的最近点映射$ p_a $和$ p_b $。我们提出了投影到其交叉点$ a \ cap b $的公式。作为一种特殊情况，我们得出了用于投影到两个超平面相交的公式。这些公式即使$ a \ cap b $是空的，也提供了有用的信息。还提供了示例和数值实验。
Let $A$ be a closed affine subspace and let $B$ be a hyperplane in a Hilbert space. Suppose we are given their associated nearest point mappings $P_A$ and $P_B$, respectively. We present a formula for the projection onto their intersection $A\cap B$. As a special case, we derive a formula for the projection onto the intersection of two hyperplanes. These formulas provides useful information even if $A\cap B$ is empty. Examples and numerical experiments are also provided.
