scholarly journals Recursive approximation of the dominant eigenspace of an indefinite matrix

2012 ◽  
Vol 236 (16) ◽  
pp. 4090-4104 ◽  
Author(s):  
Nicola Mastronardi ◽  
Paul Van Dooren
Keyword(s):  
Indefinite Matrix

On the formulation of the indefinite matrix

1968 ◽  
Vol 3 (3) ◽  
pp. 307-308
Author(s):  
W.F. Kiss ◽  
R.A. Gilson
Keyword(s):  
Indefinite Matrix

scholarly journals Moore-Penrose inverses of Gram matrices leaving a cone invariant in an indefinite inner product space

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
K. Appi Reddy ◽  
T. Kurmayya
Keyword(s):  
Product Space ◽  
Matrix Multiplication ◽  
Convex Cones ◽  
Inner Product Space ◽  
Inner Product ◽  
Indefinite Inner Product ◽  
Indefinite Matrix ◽  
Gram Matrices ◽  
Indefinite Inner Product Space

AbstractIn this paper we characterize Moore-Penrose inverses of Gram matrices leaving a cone invariant in an indefinite inner product space using the indefinite matrix multiplication. This characterization includes the acuteness (or obtuseness) of certain closed convex cones.

scholarly journals Partial factorization of a dense symmetric indefinite matrix

2011 ◽  
Vol 38 (2) ◽  
pp. 1-19 ◽  
Author(s):  
John K. Reid ◽  
Jennifer A. Scott
Keyword(s):  
Indefinite Matrix

Multi-physics flux coupling for hydraulic fracturing modelling within INMOST platform

2020 ◽  
Vol 35 (4) ◽  
pp. 223-237
Author(s):  
Kirill M. Terekhov
Keyword(s):  
Hydraulic Fracturing ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Heterogeneous Media ◽  
Saddle Point Problem ◽  
Point Problem ◽  
Indefinite Matrix ◽  
Physics Model ◽  
Stability Issues ◽  
Volume Method

AbstractThis work presents an overview of techniques that enable the construction of collocated finite volume method for complex multi-physics models in multiple domains. Each domain is characterized by the properties of heterogeneous media and features a distinctive multi-physics model. Coupling together systems of equations, corresponding to multiple unknowns, results in a vector flux. The finite volume method requires continuity of intradomain and interdomain vector fluxes. The continuous flux is derived using an extension of the harmonic averaging point concept. Often, the collocated coupling of the equations results in a saddle-point problem subject to inf-sup stability issues. These issues are addressed by the eigen-splitting of indefinite matrix coefficients encountered in the flux expression. The application of the techniques implemented within INMOST platform to hydraulic fracturing problem is demonstrated.

ON RANK ESTIMATION IN SYMMETRIC MATRICES: THE CASE OF INDEFINITE MATRIX ESTIMATORS

2007 ◽  
Vol 23 (06) ◽  
Author(s):  
Stephen G. Donald ◽  
Natércia Fortuna ◽  
Vladas Pipiras
Keyword(s):  
Symmetric Matrices ◽  
Rank Estimation ◽  
Indefinite Matrix

Indefinite matrix inequalities via matrix means

2021 ◽  
pp. 103036
Author(s):  
Jagjit Singh Matharu ◽  
Chitra Malhotra ◽  
Mohammad Sal Moslehian
Keyword(s):  
Matrix Inequalities ◽  
Indefinite Matrix ◽  
Matrix Means

scholarly journals Modified projected Newton scheme for non-convex function with simple constraints

2021 ◽  
pp. 2-2
Author(s):  
Suvra Chakraborty ◽  
Geetanjali Panda
Keyword(s):  
Convex Optimization ◽  
Local Minimum ◽  
Optimization Problem ◽  
Saddle Points ◽  
Hessian Matrix ◽  
Minimum Point ◽  
Numerical Illustration ◽  
Convex Optimization Problem ◽  
Indefinite Matrix ◽  
Local Minimum Point

In this paper, a descent line search scheme is proposed to find a local minimum point of a non-convex optimization problem with simple constraints. The idea ensures that the scheme escapes the saddle points and finally settles for a local minimum point of the non-convex optimization problem. A positive definite scaling matrix for the proposed scheme is formed through symmetric indefinite matrix factorization of the Hessian matrix of the objective function at each iteration. A numerical illustration is provided, and the global convergence of the scheme is also justified.

scholarly journals Nonnegative generalized inverses in indefinite inner product spaces

Filomat ◽  
2013 ◽  
Vol 27 (4) ◽  
pp. 659-670 ◽  
Author(s):  
Sachindranath Jayaraman
Keyword(s):  
Generalized Inverses ◽  
Inner Product ◽  
Matrix Product ◽  
Product Spaces ◽  
Indefinite Inner Product ◽  
Indefinite Matrix ◽  
Inner Product Spaces ◽  
Weak Monotonicity

The aim of this article is to investigate nonnegativity of the inverse, the Moore-Penrose inverse and other generalized inverses, in the setting of indefinite inner product spaces with respect to the indefinite matrix product. We also propose and investigate generalizations of the corresponding notions of matrix monotonicity, namely, o-(rectangular) monotonicity, o-semimonotonicity and ?-weak monotonicity and its interplay with nonnegativity of various generalized inverses in the same setting.

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