Weighted Carlson Mean of Positive Definite Matrices
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Taking the weighted geometric mean [11] on the cone of positive definite matrix, we propose an iterative mean algorithm involving weighted arithmetic and geometric means of n−positive definite matrices which is a weighted version of Carlson mean presented by Lee and Lim [13]. We show that each sequence of the weigthed Carlson iterative mean algorithm has a common limit and the common limit of satisfies weighted multidimensional versions of all properties like permutation symmetry, concavity, monotonicity, homogeneity, congruence invariancy, duality, mean inequalities
Abstract
Taking the weighted geometric mean [11] on the cone of positive definite matrix, we propose an iterative mean algorithm involving weighted arithmetic and geometric means of n−positive definite matrices which is a weighted version of Carlson mean presented by Lee and Lim [13]. We show that each sequence of the weigthed Carlson iterative mean algorithm has a common limit and the common limit of satisfies weighted multidimensional versions of all properties like permutation symmetry, concavity, monotonicity, homogeneity, congruence invariancy, duality, mean inequalities
참고문헌 (14)
- T. Ando, "Geometric means", Linear Algebra Appl., 385, pp.305~334 (2004)
- R. Bhatia, "On the exponential metric increasing property", Linear Algebra Appl, 375, pp.211~220 (2003)
- R. Bhatia, "Positive definite matrices" (2007), Princeton University Press
- D. Bini, "An effective matrix geometric mean satisfying the Ando-Li-Mathias properties", Math. Comp., 79, pp.437~452 (2010)
- C. W. Borchardt, , pp.455~462 (1881), U. Hoepli
- B. C. Carlson, "Hidden symmetries of special functions", SIAM Review, 12, pp.332~346 (1970)
- B. C. Carlson, "Algorithms involving arithmetic and geometric means", Amer. Math. Monthly, 78, pp.496~505 (1971)
- G. Corach, "Convexity of the geodesic distance on spaces of positive operators", Illinois J. Math, 38, pp.87~94 (1994)
- R. Horn, "Matrix analysis" (1985), Cambridge University Press
- S. Lang, "Fundamentals of differential geometry, Graduate Texts in Math" (1999), Springer
- J. D. Lawson, "Weighted geometric means", Forum Mathematicum, 24, pp.1067~1090 (2012)
- J. D. Lawson, "The geometric mean, matrices, metrics, and more", Amer. Math. Monthly, 108, pp.797~812 (2001)
- H. Lee, "Carlson’s iterative algorithm of positive definite matrices", Linear Algebra Appl.
- H. Lee, "Invariant metrics, contractions and nonlinear matrix equations", Nonlinearity, 21, pp.857~878 (2008)