Using numeric approximations to solve continuous problems
Numerical analysis is a branch of mathematics that solves continuous problems using numeric approximation. It involves designing methods that give approximate but accurate numeric solutions, which is useful in cases where the exact solution is impossible or prohibitively expensive to calculate. Numerical analysis also involves characterizing the convergence, accuracy, stability, and computational complexity of these methods.
MATLAB® is widely used for applied numerical analysis in engineering, computational finance, and computational biology. It provides a range of numerical methods for:
- Interpolation, extrapolation, and regression
- Differentiation and integration
- Linear systems of equations
- Eigenvalues and singular values
- Ordinary differential equations (ODEs)
- Partial differential equations (PDEs)
You can also perform fast Fourier transforms, quadrature, optimization, and linear programming with the MATLAB product family. In addition, you can create and implement your own numerical methods using the built-in support for vector and matrix operations in the MATLAB language.
Examples and How To
See also: mathematical modeling, scientific computing, Optimization Toolbox, Curve Fitting Toolbox, Partial Differential Equations Toolbox, numerical analysis videos