Physical Sciences and Mathematics Commons^™

Ramanujan–Sato Series For 1/Π, Timothy Huber, Daniel Schultz, Dongxi Ye

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We compute Ramanujan–Sato series systematically in terms of Thompson series and their modular equations. A complete list of rational and quadratic series corresponding to singular values of the parameters is derived.

The Singular Value Expansion For Compact And Non-Compact Operators, Daniel Crane

Dissertations, Master's Theses and Master's Reports

Given any bounded linear operator T : X → Y between separable Hilbert spaces X and Y , there exists a measure space (M, Α, µ) and isometries V : L²(M) → X, U : L²(M) → Y and a nonnegative, bounded, measurable function σ : M → [0, ∞) such that

T = Um_σV ^†,

with m_σ : L²(M ) → L²(M ) defined by m_σ(f ) = σf for all f …

A Multi-Step Nonlinear Dimension-Reduction Approach With Applications To Bigdata, R. Krishnan, V. A. Samaranayake, Jagannathan Sarangapani

Mathematics and Statistics Faculty Research & Creative Works

In this paper, a multi-step dimension-reduction approach is proposed for addressing nonlinear relationships within attributes. In this work, the attributes in the data are first organized into groups. In each group, the dimensions are reduced via a parametric mapping that takes into account nonlinear relationships. Mapping parameters are estimated using a low rank singular value decomposition (SVD) of distance covariance. Subsequently, the attributes are reorganized into groups based on the magnitude of their respective singular values. The group-wise organization and the subsequent reduction process is performed for multiple steps until a singular value-based user-defined criterion is satisfied. Simulation analysis is …

Computing Singular Values Of Large Matrices With An Inverse-Free Preconditioned Krylov Subspace Method, Qiao Liang, Qiang Ye

Mathematics Faculty Publications

We present an efficient algorithm for computing a few extreme singular values of a large sparse m×n matrix C. Our algorithm is based on reformulating the singular value problem as an eigenvalue problem for C^TC. To address the clustering of the singular values, we develop an inverse-free preconditioned Krylov subspace method to accelerate convergence. We consider preconditioning that is based on robust incomplete factorizations, and we discuss various implementation issues. Extensive numerical tests are presented to demonstrate efficiency and robustness of the new algorithm.

Absolute Equal Distribution Of Families Of Finite Sets, William F. Trench

William F. Trench

No abstract provided.