Continued Fraction as a Discrete Nonlinear Transform

The connection between a Taylor series and a continued-fraction involves a nonlinear relation between the Taylor coefficients $\{ a_n \}$ and the continued-fraction coefficients $\{ b_n \}$. In many instances it turns out that this nonlinear relation transforms a complicated sequence $\{a_n \}$ into a very simple one $\{ b_n \}$. We illustrate this simplification in the context of graph combinatorics.Comment: 6 pages, OKHEP-93-0

Quantifying the Effect of Matrix Structure on Multithreaded Performance of the SpMV Kernel

Sparse matrix-vector multiplication (SpMV) is the core operation in many common network and graph analytics, but poor performance of the SpMV kernel handicaps these applications. This work quantifies the effect of matrix structure on SpMV performance, using Intel's VTune tool for the Sandy Bridge architecture. Two types of sparse matrices are considered: finite difference (FD) matrices, which are structured, and R-MAT matrices, which are unstructured. Analysis of cache behavior and prefetcher activity reveals that the SpMV kernel performs far worse with R-MAT matrices than with FD matrices, due to the difference in matrix structure. To address the problems caused by unstructured matrices, novel architecture improvements are proposed.Comment: 6 pages, 7 figures. IEEE HPEC 201

Photoluminescence-based measurements of the energy gap and diffusion length of Zn_3P_2

The steady-state photoluminescence spectra of zinc phosphide (Zn_3P_2) wafers have revealed a fundamental indirect band gap at 1.38 eV, in close proximity to the direct band gap at 1.50 eV. These values are consistent with the values for the indirect and direct band gaps obtained from analysis of the complex dielectric function deduced from spectroscopic ellipsometric measurements. Bulk minority carrier lifetimes of 20 ns were observed by time-resolved photoluminescence decay measurements, implying minority-carrier diffusion lengths of ≥ 7 µm