×

On the partitioned matrix N and its associated system AX=T, A*Y+QX=Z. (English) Zbl 0458.15003

MSC:

15A09 Theory of matrix inversion and generalized inverses
15A06 Linear equations (linear algebraic aspects)
65F05 Direct numerical methods for linear systems and matrix inversion
65F20 Numerical solutions to overdetermined systems, pseudoinverses

Citations:

Zbl 0361.15007
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] 1 A BEN-ISRAEL, A note on partitioned matrix equations SIAM Rev , 11 (1969), 247-250 Zbl0175.02402 MR245593 · Zbl 0175.02402 · doi:10.1137/1011038
[2] 2 A BEN-ISRAEL, Generalized inverses theory and applications J Wiley and Sons (1974), New York Zbl0305.15001 MR396607 · Zbl 0305.15001
[3] 3 P BHIMASANKARAM, On generalized inverse of partitioned matrices, Sankhya, Ser A, 33 (1971), 311-314 Zbl0231.15011 · Zbl 0231.15011
[4] 4 A BJERHAMMAR, Theory of errors and generalized inverse matrix Elsevir Scien Public Co (1973) · Zbl 0267.65002
[5] 5 T BOULLION, P L ODELL, Generalized inverse matrices J Wiley and Sons (1971), New York Zbl0223.15002 · Zbl 0223.15002
[6] 6 F BURNS, D CARLSON, E HAYNSWORTH, T MARKHAM, A generalized inverse formula using the Schur complement, SIAM J , 26, (1974), 254-259 MR330181 · Zbl 0284.15004
[7] 7 D CARLSON, E HAYNSWORTH, T MARKHAM, A generalization of the Schur complement by means of the Moore-Penrose Inverse SIAM J Appl Math 26 (1974), 169-175 Zbl0245.15002 MR347843 · Zbl 0245.15002 · doi:10.1137/0126013
[8] 8 CHING-HSIANG HUNG, T MARKHAM, The Moore-Penrose inverse of a partitioned matrix M = A C B D Linear Alg and its Appl , 11 (1975), 73-86 Zbl0326.15005 MR369383 · Zbl 0326.15005 · doi:10.1016/0024-3795(75)90118-4
[9] 9 R E CLINE, Representation for the generalized inverse of partitioned matrix SIAM J Appl Math , 12 (1964), 588-600 Zbl0166.29902 MR172890 · Zbl 0166.29902 · doi:10.1137/0112050
[10] 10 R E CLINE, Representation of generalized inverse of sums of matrices SIAM J Num Anal , Ser B, 2 (1965), 99-114 Zbl0142.26904 · Zbl 0142.26904
[11] 11 R W COTTLE, Manifestation of the Schur complement Linear Alg and its Appl , 8 (1974), 189-211 Zbl0284.15005 · Zbl 0284.15005 · doi:10.1016/0024-3795(74)90066-4
[12] 12 T N E GREVILLE, Some applications of the pseudo-inverse of a matrix SIAM Rev , 2 (1960), 15-22 · Zbl 0168.13303
[13] 13 C HADLEY, Linear Algebra Addison-Wesley (1965), New York
[14] 14 G MARSAGLIA, G P H STYAN, Rank conditions for generalized inverses of partitioned matrices Sankhya, Ser A (1974), 437-442 Zbl0309.15002 MR384827 · Zbl 0309.15002
[15] 15 G MARSAGLIA, Equations and inequalities for ranks of matrices Linear and Multil Alg , 2 (1974), 269-292 Zbl0297.15003 · Zbl 0297.15003
[16] 16 S K MITRA, P BIMASANKHARAM, Generalized inverse of partitioned matrices and recalculation of least squares estimates for data or model charges Sankhya, Ser A, 33 (1971), 395-410 Zbl0236.62049 MR314208 · Zbl 0236.62049
[17] 17 S K MITRA, Fixed rank solutions of linear matrix equations Sankhya, Ser A, 34 (1971) 387-392 Zbl0261.15008 MR335545 · Zbl 0261.15008
[18] 18 C R RAO, Calculus of generalized inverses of matrices, Part I General Theory Sankhya, Ser A , 29 (1971), 317-342 Zbl0178.03103 · Zbl 0178.03103
[19] 19 C R RAO, S K MITRA, Generalized inverse of matrix and its application J Wiley and Sons (1971), New York · Zbl 0236.15004
[20] 20 C H ROHDE, Generalized inverse of partitioned matrices SIAM J , 13 (1965), 1033-1035 Zbl0145.03801 MR190161 · Zbl 0145.03801 · doi:10.1137/0113070
[21] 21 V VALERIO, Sulle inverse generalizzate e sulla soluzione di particolari sistemi di equazioni lineari, con applicazione al calcolo delle strutture reticolari Ace Naz Lincei, Rend sc , vol LX (1976), 84-89 Zbl0361.15007 MR460357 · Zbl 0361.15007
[22] 22 V VALERIO, On the reticulated structures calculation Seminar held at the Delhi Campus of the Indian Statistical Institute (Nov 1977) unpublished communication, to appear
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.