Conjugate Gradient (CG) is a common iterative algorithm for solving symmetric positive-definite linear systems Ax = b. Given a symmetric positive-definite matrix A, the number of iterations needed to reduce the norm of the residual by a constant factor is bounded by the spectral condition number...
25 A MIXED-NORM ESTIMATE OF TWO-PARTICLE REDUCED DENSITY MATRIX OF MANY-BODY SCHRÖD 46:42 A NON-COMMUTATIVE ENTROPIC OPTIMAL TRANSPORT APPROACH TO QUANTUM COMPOSITE SYSTE 1:40:34 APPLICATIONS OF OMT IN PROVING ISOPERIMETRIC AND SOBOLEV INEQUALITIES 55:44 RANDOM MATCHING IN 2D_ SOME RECENT ...
25 A MIXED-NORM ESTIMATE OF TWO-PARTICLE REDUCED DENSITY MATRIX OF MANY-BODY SCHRÖD 46:42 A NON-COMMUTATIVE ENTROPIC OPTIMAL TRANSPORT APPROACH TO QUANTUM COMPOSITE SYSTE 1:40:34 APPLICATIONS OF OMT IN PROVING ISOPERIMETRIC AND SOBOLEV INEQUALITIES 55:44 RANDOM MATCHING IN 2D_ SOME RECENT ...
TWO-WEIGHT NORM INEQUALITIES FOR VECTOR-VALUED OPERATORS We study two-weight norm inequalities for a vector-valued operator from a weighted L-P (sigma)-space to mixed norm L-ls(q) (mu) spaces, 1 < p < infinity, 0 < q < p. We apply these results to the boundedness of Wolff's pote...
For any positive integer n, we define ≔[n]≔{1,2,…,n}. Given a matrix X∈Rn1×n2, its rank and trace are denoted as rank(X) and tr(X). The Ky-Fan k norm ‖X‖k is defined as ≔‖X‖k≔∑i=1kσi(X), where k≤min{n1,n2} and σi(X) is the ith largest ...
These objectives can be accomplished in two‐norm (L) or one‐norm (L) or combined formats. Also included is a TR design that minimizes the effect of the standardization set composition, i.e., reduces the effect of an outlier. Ongoing work that removes all reference samples from the TR ...
This paper proposes an oriented Hausdorff similarity (OHS) measure for robust object alignment. The OHS measure is introduced by replacing the distance concept of conventional Hausdoff distance (HD) algorithms by the similarity concept of the Hough transform (HT). The proposed algorithm can be consi...
To this end, sufficient conditions for the existence of an upper bound of H-two norm are presented in terms of linear matrix inequalities. Considering uncertainty of system matrices, a robust H-two filter is designed. The proposed method is also applicable to cover the case where the ...
In particular, ρ(r) = 2πrp(x), where p(x) is the single-particle probability density for a specific particle to be at x, which turns out to depend only on the norm r = |x|. In the AOUP case, p(x) is fitted by a Gaussian centered at x = 0, while in ABP...
We formulate a density matrix to fully describe two-photon state within a thermal light source in the photon orbital angular momentum (OAM) Hilbert space. We prove the separability, i.e., zero entanglement of the thermal two-photon state. Still, we revea