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Numerical methods are a specific form of mathematics that involve creating and use of algorithms to map out the mathematical core of a practical problem. Numerical methods naturally find application in all fields of engineering, physical sciences, life sciences, social sciences, medicine, business, and even arts. The common uses of numerical methods include approximation, simulation, and estimation, and there is almost no scientific field in which numerical methods do not find a use. Results communicated here include topics ranging from statistics (Detecting Extreme Values with Order Statistics in Samples from Continuous Distributions) and Statistical software packages (dCATCH—A Numerical Package for d-Variate near G-Optimal Tchakaloff Regression via Fast NNLS) to new approaches for numerical solutions (Exact Solutions to the Maxmin Problem max‖Ax‖ Subject to ‖Bx‖≤1; On q-Quasi-Newton’s Method for Unconstrained Multiobjective Optimization Problems; Convergence Analysis and Complex Geometry of an Efficient Derivative-Free Iterative Method; On Derivative Free Multiple-Root Finders with Optimal Fourth Order Convergence; Finite Integration Method with Shifted Chebyshev Polynomials for Solving Time-Fractional Burgers’ Equations) to the use of wavelets (Orhonormal Wavelet Bases on The 3D Ball Via Volume Preserving Map from the Regular Octahedron) and methods for visualization (A Simple Method for Network Visualization).

Research & information: general --- Mathematics & science --- Clenshaw–Curtis–Filon --- high oscillation --- singular integral equations --- boundary singularities --- local convergence --- nonlinear equations --- Banach space --- Fréchet-derivative --- finite integration method --- shifted Chebyshev polynomial --- Caputo fractional derivative --- Burgers’ equation --- coupled Burgers’ equation --- maxmin --- supporting vector --- matrix norm --- TMS coil --- optimal geolocation --- probability computing --- Monte Carlo simulation --- order statistics --- extreme values --- outliers --- multiobjective programming --- methods of quasi-Newton type --- Pareto optimality --- q-calculus --- rate of convergence --- wavelets on 3D ball --- uniform 3D grid --- volume preserving map --- Network --- graph drawing --- planar visualizations --- multiple root solvers --- composite method --- weight-function --- derivative-free method --- optimal convergence --- multivariate polynomial regression designs --- G-optimality --- D-optimality --- multiplicative algorithms --- G-efficiency --- Caratheodory-Tchakaloff discrete measure compression --- Non-Negative Least Squares --- accelerated Lawson-Hanson solver --- Clenshaw–Curtis–Filon --- high oscillation --- singular integral equations --- boundary singularities --- local convergence --- nonlinear equations --- Banach space --- Fréchet-derivative --- finite integration method --- shifted Chebyshev polynomial --- Caputo fractional derivative --- Burgers’ equation --- coupled Burgers’ equation --- maxmin --- supporting vector --- matrix norm --- TMS coil --- optimal geolocation --- probability computing --- Monte Carlo simulation --- order statistics --- extreme values --- outliers --- multiobjective programming --- methods of quasi-Newton type --- Pareto optimality --- q-calculus --- rate of convergence --- wavelets on 3D ball --- uniform 3D grid --- volume preserving map --- Network --- graph drawing --- planar visualizations --- multiple root solvers --- composite method --- weight-function --- derivative-free method --- optimal convergence --- multivariate polynomial regression designs --- G-optimality --- D-optimality --- multiplicative algorithms --- G-efficiency --- Caratheodory-Tchakaloff discrete measure compression --- Non-Negative Least Squares --- accelerated Lawson-Hanson solver