Generalization of the matrix inversion lemma
- 1 July 1986
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in Proceedings of the IEEE
- Vol. 74 (7) , 1050-1052
- https://doi.org/10.1109/proc.1986.13587
Abstract
A generalized form of the matrix inversion lemma is shown which allows particular forms of this lemma to be derived simply. The relationships between this direct method for solving linear matrix equations, lower-diagonal-upper decomposition, and iterative methods such as point-Jacobi and Hotelling's method are established. The generalized form is used to derive a new factorization scheme and a new matrix inversion algorithm with a high degree of parallelism.Keywords
This publication has 12 references indexed in Scilit:
- Eddy-current sensor for DC and low-frequency magnetic fieldsProceedings of the IEEE, 1985
- On Deriving the Inverse of a Sum of MatricesSIAM Review, 1981
- The fluxgate magnetometerJournal of Physics E: Scientific Instruments, 1979
- Extension of the Gauss-Markov Theorem to Include the Estimation of Random EffectsThe Annals of Statistics, 1976
- Recent advances in fluxgate magnetometryIEEE Transactions on Magnetics, 1972
- A gamma-level portable ring-core magnetometerIEEE Transactions on Magnetics, 1971
- A fluxgate sensor of high stability for low field magnetometryIEEE Transactions on Magnetics, 1968
- Factors affecting the sensitivity of gamma-level ring-core magnetometersIEEE Transactions on Magnetics, 1965
- Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given MatrixThe Annals of Mathematical Statistics, 1950
- Some New Methods in Matrix CalculationThe Annals of Mathematical Statistics, 1943