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Stability is sometimes achieved by including numerical diffusion. Numerical diffusion is a mathematical term which ensures that roundoff and other errors in the calculation get spread out and do not add up to cause the calculation to "blow up". Von Neumann stability analysis is a commonly used procedure for the stability analysis of finite ...
It arises in the numerical analysis of explicit time integration schemes, when these are used for the numerical solution. As a consequence, the time step must be less than a certain upper bound, given a fixed spatial increment, in many explicit time-marching computer simulations ; otherwise, the simulation produces incorrect or unstable results.
Cannon's algorithm — a distributed algorithm, especially suitable for processors laid out in a 2d grid; Freivalds' algorithm — a randomized algorithm for checking the result of a multiplication; Matrix decompositions: LU decomposition — lower triangular times upper triangular; QR decomposition — orthogonal matrix times triangular matrix
The field of numerical analysis predates the invention of modern computers by many centuries. Linear interpolation was already in use more than 2000 years ago. Many great mathematicians of the past were preoccupied by numerical analysis, [5] as is obvious from the names of important algorithms like Newton's method, Lagrange interpolation polynomial, Gaussian elimination, or Euler's method.
The stability of numerical schemes can be investigated by performing von Neumann stability analysis. For time-dependent problems, stability guarantees that the numerical method produces a bounded solution whenever the solution of the exact differential equation is bounded.
It is widely used in numerical evaluation of the dynamic response of structures and solids such as in finite element analysis to model dynamic systems. The method is named after Nathan M. Newmark , [ 1 ] former Professor of Civil Engineering at the University of Illinois at Urbana–Champaign , who developed it in 1959 for use in structural ...
Data structure: String: ... In computer science, the Cocke–Younger–Kasami algorithm (alternatively called CYK, ... Numerical stability
The Lax–Friedrichs method, named after Peter Lax and Kurt O. Friedrichs, is a numerical method for the solution of hyperbolic partial differential equations based on finite differences. The method can be described as the FTCS (forward in time, centered in space) scheme with a numerical dissipation term of 1/2.