PURR Registry

32-digit values of the first 100 recurrence coefficients for orthogonal polynomials relative to the weight function w(x)=(1-x)^-1/2}x^1/2}log(1/x) on (0,1)

Computer Science Equation Table Gauss-Radau formula Jacobi polynomials Jacobi weight functions Mathematics Matlab OPQ routine Orthogonal polynomials Walter Gautschi Archives

OPCBSPL: Orthogonal polynomials relative to cardinal B-spline weight functions

10.4231/R7NG4NKC

Walter Gautschi

10/28/2016

A stable and efficient discretization procedure is developed to compute recurrence coefficients for orthogonal polynomials whose weight function is a polynomial cardinal B-spline of order greater than, or equal to, one.

B-spline Computer Science Mathematics Modification algorithms for orthogonal polynomials Orthogonal polynomials polynomials Walter Gautschi Archives weight functions

Code and Dataset for Pattern Recognition Benchmarks

10.4231/R7610X8M

Jonas Hepp , Mireille Boutin , Yellamraju Tarun

02/03/2016

This code computed a sequence of bounds for the error rate of a pattern recognition method. The bounds correspond to the error rate that one would expect to achieve by simply selecting features at random and thresholding the feature (TARP) approach.

classification Computer Science Electrical and Computer Engineering feature evaluation image processing image recognition Pattern Recognition Pedestrian Classification

32-digit values of the first 100 recurrence coefficients for an Airy weight function

10.4231/R7V122R6

Walter Gautschi

10/19/2016

32-digit values of the first 100 recurrence coefficients for the (normalized) weight function w(x)=c*x^(-5/6)e^(-x)Ai((3x/2)^(2/3)) on [0,Inf], c=2^(-1/6)*3^(1/6)/pi^(1/2), where Ai is the Airy function

Airy weight function Computer Science Mathematics Modification algorithms for orthogonal polynomials Orthogonal polynomials Quadrature and cubature formulas Walter Gautschi Archives

Squared Abel polynomials

10.4231/R74Q7RZF

Walter Gautschi

02/14/2017

Matlab routine for the first N recurrence coefficients of squared Abel polynomials

Abel polynomials Computer Science Mathematics Orthogonal polynomials Subrange Hermite polynomials Variable-precision computation Walter Gautschi Archives weight functions

Modified squared Abel polynomials

10.4231/R78C9T8V

Walter Gautschi

02/14/2017

Matlab routine for the first N recurrence coefficients of modified squared Abel polynomials

Abel polynomials Computer Science Mathematics Modification algorithms for orthogonal polynomials Orthogonal polynomials Variable-precision computation Walter Gautschi Archives weight functions

32-digit values of the first 100 recurrence coefficients for a four-parameter exponential weight function with parameters 1, 1/2, 1/2, -3/2

10.4231/R7W66HSK

Walter Gautschi

02/14/2017

32-digit values of the first 100 recurrence coefficients for the weight function (inverse Gaussian distribution) w(x)=const*x^d*exp(-b/x^a-c*x^a) on [0,Inf], const=exp(1)/√(2*π), a=1, b=c=1/2, d=-3/2

Computer Science Mathematics Modification algorithms for orthogonal polynomials moment-based method Orthogonal polynomials Walter Gautschi Archives weight functions

32-digit values of the first 100 recurrence coefficients for a four-parameter exponential weight function with parameters a=1/3, b=c=1/2, d=-7/6

10.4231/R7RF5S1T

Walter Gautschi

02/14/2017

32-digit values of the first 100 recurrence coefficients for the weight function w(x)=const*x^d*exp(-b/x^a-c*x^a), const=exp(1)/(3*√(2*pi)), a=1/3, b=c=1/2, d=-7/6

Computer Science Mathematics Modification algorithms for orthogonal polynomials moment-based method Orthogonal polynomials Walter Gautschi Archives weight functions