递归双正交化方法与正交投影
Recursive bi-orthogonalisation approach and orthogonal projectors
摘要：
提出了一种方法，给定一族线性无关的函数，构造适当的双正交集，以表示正交投影算子到相应的子空间。该过程迭代地演进，并且它被赋予以下性质：i）它产生所需的双正交函数，避免了逆运算的需要ii）它允许每次在给定集合中引入新成员时快速更新整个双正交函数族。该方法是特别相关的近似问题时产生的功能是表示为非正交波形的有限线性叠加。
英文摘要：
An approach is proposed which, given a family of linearly independent functions, constructs the appropriate biorthogonal set so as to represent the orthogonal projector operator onto the corresponding subspace. The procedure evolves iteratively and it is endowed with the following properties: i) it yields the desired biorthogonal functions avoiding the need of inverse operations ii) it allows to quickly update a whole family of biorthogonal functions each time that a new member is introduced in the given set. The approach is of particular relevance to the approximation problem arising when a function is to be represented as a finite linear superposition of non orthogonal waveforms.
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