9 papers
Tail Bounds for Functions of Weighted Tensor Sums Derived from Random Walks on Riemannian Manifolds
Shih-Yu Chang
This paper presents significant advancements in tensor analysis and the study of random walks on manifolds. It introduces new tensor inequalities derived using the Mond-Pecaric met…
Generalized Converses of Operator Jensens Inequalities with Applications to Hypercomplex Function Approximations and Bounds Algebra
Shih-Yu Chang
Mond and Pecaric proposed a powerful method, namd as MP method, to deal with operator inequalities. However, this method requires a real-valued function to be convex or concave, an…
Generalized Choi-Davis-Jensen's Operator Inequalities and Their Applications
Shih Yu Chang, Yimin Wei
The original Choi-Davis-Jensen's inequality, with its wide-ranging applications in diverse scientific and engineering fields, has motivated researchers to explore generalizations.…
Tail bounds for Multivariate Random Tensor Means
Shih-Yu Chang
In our recent research endeavors, we have delved into the realm of tail bounds problems concerning bivariate random tensor means. In this context, tensors are treated as finite-dim…
Random Tensor Inequalities and Tail bounds for Bivariate Random Tensor Means, Part II
Shih-Yu Chang
This is Part II of our work about random tensor inequalities and tail bounds for bivariate random tensor means. After reviewing basic facts about random tensors, we first consider…
Random Tensor Inequalities and Tail bounds for Bivariate Random Tensor Means, Part I
Shih-Yu Chang
In this work, we apply the concept about operator connection to consider bivariate random tensor means. We first extend classical Markov and Chebyshev inequalities from a random va…