Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Solution of quadratic matrix equations by least-squares method

Authors: Charles C. Lee and H. P. Niu
Journal: Quart. Appl. Math. 30 (1972), 345-350
MSC: Primary 65F99
DOI: https://doi.org/10.1090/qam/403194
MathSciNet review: 403194
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Abstract: A least-square method is described for obtaining the solutions $ A$ and $ B$ for the matrix equations $ {Y^2} - YD + S = 0$ and $ {Y^2} - DY + S = 0$ respectively. No limitation is set on $ A$, $ B$, $ D$, and $ S$ except that they be square matrices. An illustrated example, including computing procedures, is discussed. The mathematical solutions presented should prove useful for solving the eigenvalue problem $ \left( {{\lambda ^2}I + \lambda D + S} \right)X = 0$, especially when the dimension of the matrices is large.

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DOI: https://doi.org/10.1090/qam/403194
Article copyright: © Copyright 1972 American Mathematical Society

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