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.


References [Enhancements On Off] (What's this?)

  • [1] J. E. McFarland, An iterative solution of the quadratic equation in Banach space, Proc. Amer. Math. Soc. 9, 824-830 (1958) MR 0096147
  • [2] Wyman G. Fair, Formal continued fractions and applications, Ph.D. thesis, University of Kansas, 1968, pp. 14-45 MR 2618083
  • [3] Louis G. Kelly, Handbook of numerical methods and applications, Addison-Wesley, Reading, Mass. 1967, pp. 63-66, 127-141
  • [4] Francis Scheid, Theory and problems of numerical analysis, McGraw-Hill, New York, 1968, pp. 235-266, 294-309, 375-377

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

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