Denting the FRTB IMA Computational Challenge via Orthogonal Chebyshev Sliding Technique

Robust exact differentiation via sliding mode technique

The main problem in differentiator design is to combine differentiation exactness with robustness in respect to possible measurement errors and input noises. The proposed differentiator provides for proportionality of the maximal differentiation error to the square root of the maximal deviation of the measured input signal from the base signal. Such an order of the differentiation error is show...

Solution of six chemical engineering problems using the Chebyshev orthogonal collocation technique

The Chebyshev orthogonal collocation is a powerful and accurate numerical technique, which is also relatively easy to implement using modern mathematical software (e.g., MATHEMATICA and MATLAB). This technique allows the elucidation of engineering problems involving partial differentials equations or boundary value problems. Six chemical engineering problems concerning the transfer of momentum,...

Solving two-dimensional chemical engineering problems using the chebyshev orthogonal collocation technique

The present paper describes how to apply the Chebyshev orthogonal collocation technique to solve steady-state and unsteady-steady two-dimensional problems. All problems are solved using one single computer algebra, Mathematica . The problems include: (1) steady-state heat transfer in a rectangular bar, (2) steady-state flow in a rectangular duct, (2) steady-state heat transfer in a cooling cyli...

Outlier-Resistant L1 Orthogonal Regression via the Reformulation-Linearization Technique

Assessing the linear relationship between a set of continuous predictors and a continuous response is a well-studied problem in statistics and data mining. L2-based methods such as ordinary least squares and orthogonal regression can be used to determine this relationship. However, both of these methods become impaired when influential values are present. This problem becomes compounded when ou...

Realization of the Frolov cubature formula via orthogonal Chebyshev-Frolov lattices