Search results
Results from the WOW.Com Content Network
NumPy, a BSD-licensed library that adds support for the manipulation of large, multi-dimensional arrays and matrices; it also includes a large collection of high-level mathematical functions. NumPy serves as the backbone for a number of other numerical libraries, notably SciPy. De facto standard for matrix/tensor operations in Python.
Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m ≥ n). It is used in some forms of nonlinear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations.
The GEKKO Python package [1] solves large-scale mixed-integer and differential algebraic equations with nonlinear programming solvers (IPOPT, APOPT, BPOPT, SNOPT, MINOS). Modes of operation include machine learning, data reconciliation, real-time optimization, dynamic simulation, and nonlinear model predictive control.
See #Numerical linear algebra for linear equations. Root-finding algorithm — algorithms for solving the equation f(x) = 0 General methods: Bisection method — simple and robust; linear convergence Lehmer–Schur algorithm — variant for complex functions; Fixed-point iteration
APMonitor: APMonitor is a mathematical modeling language for describing and solving representations of physical systems in the form of differential and algebraic equations. Armadillo is C++ template library for linear algebra; includes various decompositions, factorisations, and statistics functions; its syntax ( API ) is similar to MATLAB.
The name arises for two reasons. First, the method relies on computing the solution in small steps, and treating the linear and the nonlinear steps separately (see below). Second, it is necessary to Fourier transform back and forth because the linear step is made in the frequency domain while the nonlinear step is made in the time domain.
It is generally used in solving non-linear equations like Euler's equations in computational fluid dynamics. Matrix-free conjugate gradient method has been applied in the non-linear elasto-plastic finite element solver. [7] Solving these equations requires the calculation of the Jacobian which is costly in terms of CPU time and storage. To ...
Root-finding algorithms are used to solve nonlinear equations (they are so named since a root of a function is an argument for which the function yields zero). If the function is differentiable and the derivative is known, then Newton's method is a popular choice. [16] [17] Linearization is another technique for solving nonlinear equations.