Summary
The iterative method for solving system of linear equations, due to Kaczmarz [2], is investigated. It is shown that the method works well for both singular and non-singular systems and it determines the affine space formed by the solutions if they exist. The method also provides an iterative procedure for computing a generalized inverse of a matrix.
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Tanabe, K. Projection method for solving a singular system of linear equations and its applications. Numer. Math. 17, 203–214 (1971). https://doi.org/10.1007/BF01436376
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DOI: https://doi.org/10.1007/BF01436376