Real-time computation of the eigenvector corresponding to the smallest eigenvalue of a positive definite matrix

1994 ◽  
Vol 41 (8) ◽  
pp. 550-553 ◽  
Author(s):  
Luo Fa-Long ◽  
Li Yan-Da
Keyword(s):  
Real Time ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Smallest Eigenvalue

Bounds for Characteristic Values of Positive Definite Matrices

1972 ◽  
Vol 15 (1) ◽  
pp. 51-56 ◽  
Author(s):  
P. A. Binding ◽  
W. D. Hoskins ◽  
P. J. Ponzo
Keyword(s):  
Related Problem ◽  
Geometric Mean ◽  
General Setting ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Arithmetic Mean ◽  
Positive Real ◽  
Positive Definite Matrices ◽  
Smallest Eigenvalue ◽  
Characteristic Values

We consider the problem of determining the best possible bounds on the eigenvalues of an nth order positive definite matrix B, when the determinant (D) and trace (T) are given. A large variety of bounds on the eigenvalues are known when different information concerning B is available (see, for example, [1], [2]). Since D and T simply provide the geometric mean and arithmetic mean of the positive, real eigenvalues of B, the solution to the problem involves certain inequalities satisfied by these means (see [3] for such inequalities in a more general setting). A related problem in which the largest and smallest eigenvalue are known, and inequalities involving D and T are obtained, is described in [4].

scholarly journals A geometric statement of the Harnack inequality for a degenerate Kolmogorov equation with rough coefficients

2019 ◽  
Vol 21 (07) ◽  
pp. 1850057 ◽  
Author(s):  
Francesca Anceschi ◽  
Michela Eleuteri ◽  
Sergio Polidoro
Keyword(s):  
Maximum Principle ◽  
Harnack Inequality ◽  
Weak Solutions ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Strong Maximum Principle ◽  
Kolmogorov Equation ◽  
Measurable Coefficients ◽  
Rough Coefficients ◽  
Vector Formula

We consider weak solutions of second-order partial differential equations of Kolmogorov–Fokker–Planck-type with measurable coefficients in the form [Formula: see text] where [Formula: see text] is a symmetric uniformly positive definite matrix with bounded measurable coefficients; [Formula: see text] and the components of the vector [Formula: see text] are bounded and measurable functions. We give a geometric statement of the Harnack inequality recently proved by Golse et al. As a corollary, we obtain a strong maximum principle.

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