Updating the inverse of a matrix hager
This research was supported in part by the National Science Foundation, under grant ECS-8803061, while the author was at the University of Arizona, and by the Natural Science and Engineering Research Council of Canada, under grant OPG-0105560.
In linear algebra an n-by-n (square) matrix A is called invertible (some authors use nonsingular or nondegenerate) if there exists an n-by-n matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.where A, U, C and V all denote matrices of the correct (conformable) sizes.Specifically, A is n-by-n, U is n-by-k, C is k-by-k and V is k-by-n.Stratigraphic Framework for Basin-Margin, Sub-Unconformity Diagenesis Below the Acadian Unconformity in the Southern Williston Basin, David M. Update of Horizontal Plays in Wyoming, Andrew Finley, #10980 (2017). Petroleum Systems Modelling of the Perth Basin, Western Australia, Khwaja A. San Andres Play in the Northwest Shelf of the Permian Basin: A New Insight on Its Petroleum Systems from Oil Geochemistry, Lucia M. The Paradox Salt Basin, Utah and Colorado: Recognition of New Types of Salt Structures and Their Impact on Salt-Related Traps, Katherine A. Ordovician-Aged Liquid-Rich Shales and Hydrothermal Dolomites Plays: An Updated Review of the Eastern Canada Anticosti Basin Hydrocarbon Potential, Jean-Sébastien Marcil, Jérémie Lavoie, Nabila Mechti, Peter K. Review of Mesozoic Exploration Plays in the Montenegro – NW Albania Segment of South Adriatic Basin, Zamir Bega and Z. Unlocking Reserves from a Secondary Reservoir in a Mature Field Through Integration and Engineering Approach: A Case Study from Oriente Basin, M-2 Reservoir, Eden-Yuturi Oilfield, Ecuador, Nestor Vasconez, Luciano Bravo, Ricardo Grijalva, Raul Jose Baez, Anne Valdez, Esteban Alba, Diego Tapia, Jonny Lomas, and Martha Castillo, #10978 (2017). Giles, Thomas Hearon, Mark Rowan, and Rip Langford, #10959 (2017). Dorrins, Bertrand Marcotte, and Jean-Yves Lavoie, #10555 (2013). If this is the case, then the matrix B is uniquely determined by A and is called the inverse of A, denoted by A.
A New Exploration Direction of North in Tarim Basin, China: An Enlightenment from Geochemical Characteristics of Deep Natural Gases, Wei Li, Jianfa Chen, Huayong Chen, Xinjian Zhu, and Ling Wu, #10989 (2017).
The chemical analysis showed that all the samples had high percentages of silica and alumina, thereby classifying them as Alumino-silicates.
The values for specific gravity, bulk density, solid density and apparent porosity averaged 2.75, 2.04 g/cm3 , 3.18 g/cm3 , and 13% respectively and they were within the internationally accepted range.
Alternative names for this formula are the matrix inversion lemma, Sherman–Morrison–Woodbury formula or just Woodbury formula.
However, the identity appeared in several papers before the Woodbury report.
In this paper we present an analytical forms for the inversion of general periodic tridiagonal matrices, and provide some very simple analytical forms which immediately lead to closed formulae for some special cases such as symmetric or perturbed Toeplitz for both periodic and non-periodic tridiagonal matrices.