Numerical Analysis Functions

BSPLINE function

computes a B-spline basis

FFT function

performs the finite Fourier transform

FROOT function

finds zeros of a univariate function by using a numerical root-finding method

IFFT function

computes the inverse finite Fourier transform

JROOT function

computes the first nonzero roots of a Bessel function of the first kind and the derivative of the Bessel function at each root

NORM function

computes a vector or matrix norm

ODE call

performs numerical integration of first-order vector differential equations with initial boundary conditions

ORPOL function

generates orthogonal polynomials on a discrete set of data

ORTVEC call

provides columnwise orthogonalization by the Gram-Schmidt process and stepwise QR decomposition by the Gram-Schmidt process

POLYROOT function

finds zeros of a real polynomial

PRODUCT function

multiplies matrices of polynomials

QUAD call

performs numerical integration of scalar functions in one dimension over infinite, connected semi-infinite, and connected finite intervals

RATIO function

divides matrix polynomials

SPLINE call

fits a cubic spline to data

SPLINEC call

fits a cubic spline to data and returns the spline coefficients

SPLINEV function

evaluates a cubic spline at new data points

TPSPLINE call

computes thin-plate smoothing splines

TPSPLNEV call

evaluates the thin-plate smoothing spline at new data points