Parallel Statistic Computing with Matrix: A note of Statistical Inference and Distributed Matrix Optimization

Modern-day large-scale data science demands tight integration of matrix theory, high-dimensional probability, and parallel-distributed optimization. “Parallel Statistical Computing with Matrix” offers a systematic, self‑contained treatment of core mathematical tools, algorithms, and theory underpinning high-performance statistical computing. This book covers fundamental matrix computations including matrix decompositions, nonnegative matrix factorization, tensor algebra, and randomized matrix methods. It develops high-dimensional probability and matrix concentration inequalities (Chernoff, Hoeffding, Bernstein, matrix-valued concentration results), before moving to classical and modern iterative solvers for large linear systems, pseudospectra, symmetric eigenvalue problems, matrix functions, preconditioning techniques, and distributed optimization algorithms. Suitable for graduate students and researchers in mathematics, statistics, data science, and engineering, this volume equips readers with both theoretical insight and practical algorithmic knowledge for analyzing and implementing parallel statistical-matrix computations.