%0 Journal Article %1 moler1973algorithm %A Moler, C. B. %A Stewart, G. W. %D 1973 %I Society for Industrial & Applied Mathematics (SIAM) %J SIAM Journal on Numerical Analysis %K 65f15-numerical-eigenvalues-eigenvectors %N 2 %P 241--256 %R 10.1137/0710024 %T An Algorithm for Generalized Matrix Eigenvalue Problems %U https://doi.org/10.1137%2F0710024 %V 10 %X A new method, called the $QZ$ algorithm, is presented for the solution of the matrix eigenvalue problem $Ax = Bx$ with general square matrices A and B. Particular attention is paid to the degeneracies which result when B is singular. No inversions of B or its submatrices are used. The algorithm is a generalization of the $QR$ algorithm, and reduces to it when $B = I$. Problems involving higher powers of $$ are also mentioned.

@article{moler1973algorithm, abstract = { A new method, called the $QZ$ algorithm, is presented for the solution of the matrix eigenvalue problem $Ax = \lambda Bx$ with general square matrices A and B. Particular attention is paid to the degeneracies which result when B is singular. No inversions of B or its submatrices are used. The algorithm is a generalization of the $QR$ algorithm, and reduces to it when $B = I$. Problems involving higher powers of $\lambda $ are also mentioned.}, added-at = {2020-07-13T08:53:30.000+0200}, author = {Moler, C. B. and Stewart, G. W.}, biburl = {https://www.bibsonomy.org/bibtex/203496d0de4af8769cc793f2f267d67c8/gdmcbain}, doi = {10.1137/0710024}, interhash = {f5fdabd1370b85b3beedfeeef6eb4f2a}, intrahash = {03496d0de4af8769cc793f2f267d67c8}, journal = {{SIAM} Journal on Numerical Analysis}, keywords = {65f15-numerical-eigenvalues-eigenvectors}, month = apr, number = 2, pages = {241--256}, publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})}, timestamp = {2020-07-13T08:54:03.000+0200}, title = {An Algorithm for Generalized Matrix Eigenvalue Problems}, url = {https://doi.org/10.1137%2F0710024}, volume = 10, year = 1973 }