The Numerical Algorithms Group (NAG) announced new functionality added to its numerical library for Fortran. The new functionality included at Mark 24 of the library brings the number of available routines to over 1,700, all of which are documented and includes extensions in the areas of multivariate methods, optimization, wavelet transforms, time series analysis, random number generators, special functions, correlation and regression analysis, eigenvalues and eigenvectors and operational research.
The library contains new routines that have been added in response to customer requests, and further enhancements contributed by NAG's expert developers and collaborators.
The multi-start (global) optimization routine employs a sequential QP algorithm to find, from a number of different starting points, the minimum of a general nonlinear function subject to linear, nonlinear and simple bound constraints.
The second multi-start routine is based upon a nonlinearly constrained, nonlinear sum of squares local optimizer. This global optimizer can also return the best few solutions found, mirroring the advantages of the other, more general, routine.
Adding to the existing nearest correlation matrix functionality in the NAG Library is the "individually weighted elements" nearest correlation matrix routine. This routine allows the user to weight individual elements in their approximate correlation matrix. It can also force the computed correlation matrix to be positive definite, required by some applications to improve the condition of the matrix.
Routines to evaluate the confluent hypergeometric function, commonly found in many applications including option pricing, have been included. These routines have been designed to provide high accuracy solutions over a large range of input parameters. The may be used to determine scaled solutions for when the value of the function is not explicitly representable.
Mark 24 also features the first part of collaborative work with the University of Strathclyde. The new functionality sits in the curve and surface fitting chapter; it may be used to compute a spline approximation to a set of scattered data, which it does using a two stage approximation method (shown in the image above).
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Sources: Press materials received from the company and additional information gleaned from the company's website.