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Generalized inverses of certain Toeplitz matrices. (English) Zbl 0273.15004

MSC:
15A09Matrix inversion, generalized inverses
15B48Positive matrices and their generalizations; cones of matrices
15A30Algebraic systems of matrices
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Full Text: DOI
References:
[1] Bareiss, E. H.: Numerical solution of linear equations with Toeplitz and vector Toeplitz matrices. Numer. math. 13, 404-424 (1969) · Zbl 0174.20401
[2] Bellman, R.: Introduction to matrix analysis. (1960) · Zbl 0124.01001
[3] Ben Israel, A.; Charnes, A.: Contributions to the theory of generalized inverses. J. soc. Ind. and appl. Math. 11, 588-600 (1963) · Zbl 0116.32202
[4] Ben Israel, A.; Charnes, A.: Matrices of index 0 and 1. SIAM J. Appl. math. 17, 1118-1122 (1969)
[5] Calais, J. L.; Appel, K.: Inversion of cyclic matrices. J. math. Phys. 5, 1001-1008 (1969) · Zbl 0151.34405
[6] Chao, C. Y.: A remark on cyclic matrices. Lin. alg. And appl. 3, 157-164 (1970) · Zbl 0205.04703
[7] Cline, R. E.: Inverses of rank invariant powers of a matrix. SIAM J. Numer. anal. 5, 182-197 (1968) · Zbl 0165.34602
[8] Good, I. J.: On the inversion of circulant matrices. Biometrica 37, 185-186 (1950) · Zbl 0037.14502
[9] Greville, T. N. E.: Some applications of the pseudo-inverse of a matrix. SIAM rev. 2, 15-22 (1960) · Zbl 0168.13303
[10] Greville, T. N. E.: Some new generalized inverses with spectral properties. Proc. of the conf. On generalized matrix inverses (March, 1968) · Zbl 0227.15004
[11] Huang, N.; Cline, R. E.: Inversion of persymmetric matrices having Toeplitz inverses. J. ACM 19, 437-444 (1972) · Zbl 0259.65032
[12] Ore, O.: Some studies on cyclic determinants. Duke math. J. 18, 343-354 (1951) · Zbl 0042.24903
[13] Penrose, R.: A generalized inverse for matrices. Proc. Cambridge phil. Soc. 51, 404-413 (1955) · Zbl 0065.24603
[14] Scroggs, J. E.; Odell, P. L.: An alternate definition of a pseudo-inverse of a matrix. J. soc. Ind. and appl. Math. 14, 796-810 (1966) · Zbl 0196.30103
[15] Trench, W. F.: An algorithm for the inversion of finite Toeplitz matrices. J. soc. Ind. and appl. Math. 12, 515-523 (1964) · Zbl 0131.36002