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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).
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Keywords
- accelerated Lawson-Hanson solver
- Banach space
- boundary singularities
- Burgers’ equation
- Caputo fractional derivative
- Caratheodory-Tchakaloff discrete measure compression
- Clenshaw–Curtis–Filon
- composite method
- coupled Burgers’ equation
- D-optimality
- derivative-free method
- extreme values
- finite integration method
- Fréchet-derivative
- G-efficiency
- G-optimality
- graph drawing
- high oscillation
- local convergence
- Mathematics & science
- matrix norm
- maxmin
- methods of quasi-Newton type
- Monte Carlo simulation
- multiobjective programming
- multiple root solvers
- multiplicative algorithms
- multivariate polynomial regression designs
- network
- Non-Negative Least Squares
- nonlinear equations
- optimal convergence
- optimal geolocation
- order statistics
- outliers
- Pareto optimality
- planar visualizations
- probability computing
- q-calculus
- rate of convergence
- Reference, information & interdisciplinary subjects
- Research & information: general
- shifted Chebyshev polynomial
- singular integral equations
- supporting vector
- TMS coil
- uniform 3D grid
- volume preserving map
- wavelets on 3D ball
- weight-function
Links
DOI: 10.3390/books978-3-03943-319-3Editions