Dr. Gleb Beliakov: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=42918
en-us2015 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemWed, 05 Aug 2015 06:29:48 GMTWed, 05 Aug 2015 06:29:48 GMTNew applications published by Dr. Gleb Beliakovhttp://www.mapleprimes.com/images/mapleapps.gifDr. Gleb Beliakov: New Applications
http://www.maplesoft.com/applications/author.aspx?mid=42918
LibLip - multivariate scattered data interpolation and smoothing
http://www.maplesoft.com/applications/view.aspx?SID=4854&ref=Feed
LibLip is a Maple toolbox, which provides many methods to interpolate scattered data (with or without preprocessing) by using only the data itself and one additional parameter - the Lipschitz constant (which is basically the upper bound on the slope of the function). The Lipschitz constant can be automatically estimated from the data.
LibLip also provides approximation methods using locally Lipschitz functions.
If the data contains noise, it can be smoothened using special techniques which rely on linear programming. Lipschitz constant can
also be estimated from noisy data by using sample splitting and cross-validation.
In addition LibLip also accommodates monotonicity and range constraints. It is useful for approximation of functions that are known to be monotone with respect to all or a subset of variables, as well as monotone only on parts of the domain. Range constraints accommodate non-constant bounds on the values of the data and the interpolant.<img src="/view.aspx?si=4854/image.jpg" alt="LibLip - multivariate scattered data interpolation and smoothing" align="left"/>LibLip is a Maple toolbox, which provides many methods to interpolate scattered data (with or without preprocessing) by using only the data itself and one additional parameter - the Lipschitz constant (which is basically the upper bound on the slope of the function). The Lipschitz constant can be automatically estimated from the data.
LibLip also provides approximation methods using locally Lipschitz functions.
If the data contains noise, it can be smoothened using special techniques which rely on linear programming. Lipschitz constant can
also be estimated from noisy data by using sample splitting and cross-validation.
In addition LibLip also accommodates monotonicity and range constraints. It is useful for approximation of functions that are known to be monotone with respect to all or a subset of variables, as well as monotone only on parts of the domain. Range constraints accommodate non-constant bounds on the values of the data and the interpolant.4854Fri, 29 Dec 2006 00:00:00 ZDr. Gleb BeliakovDr. Gleb BeliakovRanLip - black-box non-uniform random variate generator
http://www.maplesoft.com/applications/view.aspx?SID=4849&ref=Feed
RanLip is a toolbox for generation of nonuniform random variates from arbitrary Lipschitz-continuous distributions in Maple environment. It uses acceptance/ rejection approach, which is based on approximation of the probability density function from above with a "hat" function. RanLip provides very fast preprocessing and generation times, and yields small rejection constant. It exhibits good performance for up to five variables, and provides the user with a black box nonuniform random variate generator for a large class of distributions, in particular, multimodal distributions.<img src="/view.aspx?si=4849/ranlib.jpg" alt="RanLip - black-box non-uniform random variate generator" align="left"/>RanLip is a toolbox for generation of nonuniform random variates from arbitrary Lipschitz-continuous distributions in Maple environment. It uses acceptance/ rejection approach, which is based on approximation of the probability density function from above with a "hat" function. RanLip provides very fast preprocessing and generation times, and yields small rejection constant. It exhibits good performance for up to five variables, and provides the user with a black box nonuniform random variate generator for a large class of distributions, in particular, multimodal distributions.4849Wed, 13 Dec 2006 00:00:00 ZDr. Gleb BeliakovDr. Gleb Beliakov