IMSL Mathematics Reference Guide

PV‑WAVE IMSL Mathematics is a powerful tool for mathematical, statistical, and scientific computing. This PV-WAVE IMSL Mathematics Reference documents the routines that support this functionality. Each function and procedure is designed for use in research as well as in technical applications.

The topics in this guide are organized as follows:

Introduction—Introduces PV-WAVE IMSL Mathematics and covers some of the basic concepts found in this guide.

Linear Systems—Discusses real and complex, full and sparse matrices, linear least squares, matrix decompositions, generalized inverses and vector-matrix operations.

Eigensystem Analysis—Discusses eigenvalues and eigenvectors of complex, real symmetric and complex Hermitian matrices.

Interpolation and Approximation—Discusses constrained curve-fitting splines, cubic splines, least-squares approximation and smoothing, and scattered data interpolation.

Quadrature—Discusses univariate, multivariate, Gauss quadrature and quasi-Monte Carlo.

Differential Equations—Discusses Adams- Gear and Runge-Kutta methods for stiff and non-stiff ordinary differential equations and support for partial differential equations.

Transforms—Discusses real and complex, one- and two-dimensional fast Fourier transforms, as well as convolutions, correlations and Laplace transforms.

Nonlinear Equations—Discusses zeros and root finding of polynomials, zeros of a function and root of a system of equations.

Optimization—Discusses unconstrained and linearly and nonlinearly constrained minimizations and the fastest linear programming algorithm available in a general math library.

Special Functions—Discusses error and gamma functions; elliptic and Fresnel integrals; basic financial functions; and Hermite, Kelvin, and Legendre functions.

Basic Statistics and Random Number Generation—Discusses Goodness-of-fit tests and random number generation.

Probability Distribution Functions and Inverses—Discusses probability distribution functions and inverses.

Utilities—Discusses machine, mathematical, physical constants, retrieval of machine constants and customizable error handling.

References—Lists the references used in this document.

Summary of Routines—Lists a summary of the routines referenced in this document.

Version 2017.0