@article{93871d48557e415a990a3d01f91223b3,

title = "Pin-pointing solution of ill-conditioned square systems of linear equations",

abstract = "A new method is proposed for an accurate solution of nearly singular systems of linear equations. The method uses the truncated singular value decomposition of the initial coefficient matrix at the first stage and the Gaussian elimination procedure for a well-conditioned reduced system of linear equations at the last stage. In contrast to various regularization techniques, the method does not require any additional physical information on the problem.",

keywords = "Accuracy, Hilbert matrix, Ill-conditioned systems, Nullspace, Singular value decomposition",

author = "Volokh, {K. Y.} and O. Vilnay",

note = "Funding Information: where A is an m x m coefficients' matrix and x and b are vectors of unknowns and right-hand sides, correspondingly. Unfortunately, existing methods may lead to inaccurate solution of (1) where matrix A is ill conditioned, The latter happens rather frequently in physics, engineering, and other branches of science. Solving (1) with standard software, the following warning: {"}results for solution of ill-conditioned matrix may contain significant numerical error{"}, often appears. The obvious method of overcoming this problem is to scale matrix A appropriately. However, {"}... the The authors are grateful to Prof. A. Sidi for his interest in the work and useful discussion. This research was supported by the Fund for the Promotion of Research at the Technion.",

year = "2000",

month = jan,

day = "1",

doi = "10.1016/S0893-9659(00)00086-0",

language = "English",

volume = "13",

pages = "119--124",

journal = "Applied Mathematics Letters",

issn = "0893-9659",

publisher = "Elsevier Ltd.",

number = "7",

}