ABSTRACT

In this paper, an operator iterative procedure for constructing an orthogonal projection of a vector onto a given subspace is proposed. The algorithm is based on Euclidean orthogonalization of power sequences of a special linear transform generated by an initial subspace. A numerical method based on this idea for solving consistent systems of linear algebraic equations is proposed. Numerical results are presented.

中文翻译：

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正交投影仪和线性代数方程组

摘要

在本文中，提出了一种将向量正交投影到给定子空间上的算子迭代程序。该算法基于由初始子空间生成的特殊线性变换的幂序列的欧几里德正交化。提出了一种基于该思想的数值方法，用于求解线性代数方程的一致系统。给出了数值结果。