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The condition number is derived from the theory of propagation of uncertainty, and is formally defined as the value of the asymptotic worst-case relative change in output for a relative change in input. The "function" is the solution of a problem and the "arguments" are the data in the problem. The condition number is frequently applied to ...
In mathematics, and in particular linear algebra, the Moore–Penrose inverse of a matrix , often called the pseudoinverse, is the most widely known generalization of the inverse matrix. [ 1 ] It was independently described by E. H. Moore in 1920, [ 2 ] Arne Bjerhammar in 1951, [ 3 ] and Roger Penrose in 1955. [ 4 ]
Conjugate gradient, assuming exact arithmetic, converges in at most n steps, where n is the size of the matrix of the system (here n = 2). In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-semidefinite.
Hilbert matrix. In linear algebra, a Hilbert matrix, introduced by Hilbert (1894), is a square matrix with entries being the unit fractions. For example, this is the 5 × 5 Hilbert matrix: The entries can also be defined by the integral. that is, as a Gramian matrix for powers of x. It arises in the least squares approximation of arbitrary ...
Gauss–Seidel method. In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel.
Preconditioner. In mathematics, preconditioning is the application of a transformation, called the preconditioner, that conditions a given problem into a form that is more suitable for numerical solving methods. Preconditioning is typically related to reducing a condition number of the problem.
The condition number of a problem is the ratio of the relative change in the solution to the relative change in the input. [3]
The stiffness matrix is the n -element square matrix A defined by. By defining the vector F with components the coefficients ui are determined by the linear system Au = F. The stiffness matrix is symmetric, i.e. Aij = Aji, so all its eigenvalues are real. Moreover, it is a strictly positive-definite matrix, so that the system Au = F always has ...