SYMINV: An Algorithm for the Inversion of a Positive Definite Matrix by the Cholesky Decomposition

Econometrica ◽  
1972 ◽  
Vol 40 (5) ◽  
pp. 961 ◽  
Author(s):  
Terry Seaks
Keyword(s):  
Positive Definite Matrix ◽  
Cholesky Decomposition ◽  
Positive Definite

scholarly journals Performance estimation of linear algebra numerical libraries

2015 ◽  
Vol 23 (1) ◽  
Author(s):  
Alessandro De Rosis
Keyword(s):  
Sparse Matrix ◽  
Positive Definite Matrix ◽  
Cholesky Decomposition ◽  
Positive Definite ◽  
Performance Estimation ◽  
Matrix Product ◽  
Cpu Time ◽  
The Matrix ◽  
Speed Up ◽  
Dense Matrices

AbstractIn this work, numerical algebraic operations are performed by using several libraries whose algorithm are optimized to drain resources from hardware architecture. In particular, dot product of two vectors and the matrix-matrix product of two dense matrices are computed. In addition, the Cholesky decomposition on a real, symmetric, and positive definite matrix is performed through routines for band and sparse matrix storage. The involved CPU time is used as an indicator of the performance of the employed numerical tool. Results are compared to naive implementations of the same numerical algorithm, highlighting the speed-up due to the usage of optimized routines.

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.

A polynomial algorithm for the quadratic programming problem

2014 ◽  
Vol 29 (3) ◽  
Author(s):  
Valentin A. Bereznev
Keyword(s):  
Computational Complexity ◽  
Quadratic Form ◽  
Quadratic Programming ◽  
Programming Problem ◽  
Polynomial Complexity ◽  
Polynomial Algorithm ◽  
Positive Definite Matrix ◽  
Positive Definite ◽  
Quadratic Programming Problem ◽  
Convex Polyhedral Cone

AbstractAn approach based on projection of a vector onto a pointed convex polyhedral cone is proposed for solving the quadratic programming problem with a positive definite matrix of the quadratic form. It is proved that this method has polynomial complexity. A method is said to be of polynomial computational complexity if the solution to the problem can be obtained in N

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