Enhance Your Learning with Numerical Analysis Flash Cards for quick understanding
A branch of mathematics that deals with the development, analysis, and implementation of algorithms for solving mathematical problems using numerical methods.
Numerical algorithms used to find the roots or solutions of equations, such as the bisection method, Newton's method, and the secant method.
Techniques used to estimate or approximate the values of a function between known data points, such as polynomial interpolation and least squares approximation.
The process of approximating the definite integral of a function using numerical methods, such as the trapezoidal rule, Simpson's rule, and Gaussian quadrature.
The process of approximating the derivative of a function using numerical methods, such as finite difference approximations and Richardson extrapolation.
Methods for solving systems of linear equations, such as Gaussian elimination, LU decomposition, and iterative methods like Jacobi and Gauss-Seidel.
Problems involving the computation of eigenvalues and eigenvectors of matrices, with applications in physics, engineering, and data analysis.
Equations that describe the rate of change of a function with respect to an independent variable, solved using numerical methods like Euler's method and Runge-Kutta methods.
Equations that involve partial derivatives of a function, often used to model physical phenomena, and solved using numerical techniques like finite difference methods and finite element methods.
Algorithms used to find the maximum or minimum of a function, such as gradient descent, Newton's method, and genetic algorithms.
Properties of numerical methods that ensure the accuracy and reliability of the computed solutions, including stability, consistency, and convergence.
The study of the errors introduced by numerical methods, including round-off errors, truncation errors, and their propagation throughout the computation.
The analysis of the computational resources required by numerical algorithms, such as time complexity and space complexity, to solve problems of varying sizes.
Techniques for performing numerical computations on multiple processors or computers simultaneously, to improve performance and solve larger problems.
The use of numerical methods and algorithms in various fields, including physics, engineering, finance, computer graphics, data analysis, and scientific computing.
A numerical technique for solving partial differential equations by dividing the problem domain into smaller elements and approximating the solution within each element.
Statistical techniques that use random sampling to estimate numerical results, often used in simulations, optimization, and solving high-dimensional problems.
A factorization of a matrix into the product of three matrices, used in various numerical algorithms, such as data compression, image processing, and recommendation systems.
An efficient algorithm for computing the discrete Fourier transform of a sequence or signal, widely used in signal processing, image analysis, and data compression.
Problems that involve finding a solution to a differential equation subject to specified boundary conditions, often solved using numerical methods like shooting methods and finite difference methods.
Numerical algorithms that solve equations or systems of equations by repeatedly improving an initial guess, such as the Jacobi method, Gauss-Seidel method, and conjugate gradient method.
The property of a numerical algorithm to produce accurate results even in the presence of small perturbations or errors in the input data or computations.
Numerical algorithms that dynamically adjust their parameters or refine their approximations based on the local behavior of the function or solution, to improve accuracy and efficiency.
Decompositions of a matrix into the product of simpler matrices, used in various numerical algorithms, such as LU decomposition, QR decomposition, and Cholesky decomposition.