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Predictor–corrector methods for solving ODEs. When considering the numerical solution of ordinary differential equations (ODEs), a predictor–corrector method typically uses an explicit method for the predictor step and an implicit method for the corrector step. Example: Euler method with the trapezoidal rule
Prism correction is measured in prism dioptres. A prescription that specifies prism correction will also specify the "base". The base is the thickest part of the lens and is opposite from the apex. Light will be bent towards the base and the image will be shifted towards the apex.
The MacCormack method is designed to solve hyperbolic partial differential equations of the form. To update this equation one timestep on a grid with spacing at grid cell , the MacCormack method uses a "predictor step" and a "corrector step", given below [3]
The basic steps in the solution update are as follows: Set the boundary conditions. Compute the gradients of velocity and pressure. Solve the discretized momentum equation to compute the intermediate velocity field. Compute the uncorrected mass fluxes at faces. Solve the pressure correction equation to produce cell values of the pressure ...
In mathematics (specifically linear algebra), the Woodbury matrix identity, named after Max A. Woodbury, says that the inverse of a rank-k correction of some matrix can be computed by doing a rank-k correction to the inverse of the original matrix.
Algorithm steps. Flow chart of PISO algorithm. The algorithm can be summed up as follows: Set the boundary conditions. Solve the discretized momentum equation to compute an intermediate velocity field. Compute the mass fluxes at the cells faces. Solve the pressure equation. Correct the mass fluxes at the cell faces.
In one dimension, solving for and applying the Newton's step with the updated value is equivalent to the secant method. The various quasi-Newton methods differ in their choice of the solution to the secant equation (in one dimension, all the variants are equivalent).
The conjugate gradient method with a trivial modification is extendable to solving, given complex-valued matrix A and vector b, the system of linear equations = for the complex-valued vector x, where A is Hermitian (i.e., A' = A) and positive-definite matrix, and the symbol ' denotes the conjugate transpose.
Suppose that we want to solve the equation f(x) = 0. As with the bisection method, we need to initialize Dekker's method with two points, say a 0 and b 0 , such that f ( a 0 ) and f ( b 0 ) have opposite signs.
In mathematics and computing, the Levenberg–Marquardt algorithm (LMA or just LM), also known as the damped least-squares (DLS) method, is used to solve non-linear least squares problems. These minimization problems arise especially in least squares curve fitting .