An Algorithm for Generalized Matrix Eigenvalue Problems.

作者: C. B. Moler , G. W. Stewart

DOI: 10.1137/0710024

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摘要: A new method, called the $QZ$ algorithm, is presented for solution of matrix eigenvalue problem $Ax = \lambda Bx$ with general square matrices and B. Particular attention paid to degeneracies which result when B singular. No inversions or its submatrices are used. The algorithm a generalization $QR$ reduces it $B I$. Problems involving higher powers $\lambda $ also mentioned.

参考文章(8)
Roger S. Martin, J. H. Wilkinson, Similarity reduction of a general matrix to Hessenberg form Numerische Mathematik. ,vol. 12, pp. 349- 368 ,(1968) , 10.1007/BF02161358
J. G. F. Francis, The QR Transformation A Unitary Analogue to the LR Transformation—Part 1 The Computer Journal. ,vol. 4, pp. 265- 271 ,(1961) , 10.1093/COMJNL/4.3.265
J. H. Wilkinson, The algebraic eigenvalue problem ,(1965)
G. Fix, R. Heiberger, An Algorithm for the Ill-Conditioned Generalized Eigenvalue Problem SIAM Journal on Numerical Analysis. ,vol. 9, pp. 78- 88 ,(1972) , 10.1137/0709009
Alston S. Householder, Unitary Triangularization of a Nonsymmetric Matrix Journal of the ACM. ,vol. 5, pp. 339- 342 ,(1958) , 10.1145/320941.320947
G. Peters, J. H. Wilkinson, Eigenvectors of real and complex matrices byLR andQR triangularizations Numerische Mathematik. ,vol. 16, pp. 181- 204 ,(1970) , 10.1007/BF02219772
R. S. Martin, J. H. Wilkinson, Reduction of the symmetric eigenproblemAx=λBx and related problems to standard form Numerische Mathematik. ,vol. 11, pp. 99- 110 ,(1968) , 10.1007/BF02165306
E. I., J. H. Wilkinson, The Algebraic Eigenvalue Problem Mathematics of Computation. ,vol. 20, pp. 621- ,(1966) , 10.2307/2003558