Ad
related to: linear equation solver wolfram x
Search results
Results from the WOW.Com Content Network
Lis (Library of Iterative Solvers for linear systems; pronounced lis]) is a scalable parallel software library to solve discretized linear equations and eigenvalue problems that mainly arise from the numerical solution of partial differential equations using iterative methods.
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.
A system of linear equations = consists of a known matrix and a known vector. To solve the system is to find the value of the unknown vector x {\displaystyle {\mathbf {x}}} . [ 3 ] [ 5 ] A direct method for solving a system of linear equations is to take the inverse of the matrix A {\displaystyle A} , then calculate x = A − 1 b {\displaystyle ...
When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set. For linear equations, logical independence is the same as linear independence. The equations x − 2y = −1, 3x + 5y = 8, and 4x + 3y = 7 are linearly dependent. For example ...
Mathematically, linear least squares is the problem of approximately solving an overdetermined system of linear equations A x = b, where b is not an element of the column space of the matrix A. The approximate solution is realized as an exact solution to A x = b' , where b' is the projection of b onto the column space of A .
In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced / ʃ ə ˈ l ɛ s k i / shə-LES-kee) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations.
Systems of linear equations arose in Europe with the introduction in 1637 by René Descartes of coordinates in geometry. In fact, in this new geometry, now called Cartesian geometry, lines and planes are represented by linear equations, and computing their intersections amounts to solving systems of linear equations.
Modified Richardson iteration is an iterative method for solving a system of linear equations. Richardson iteration was proposed by Lewis Fry Richardson in his work dated 1910. It is similar to the Jacobi and Gauss–Seidel method. We seek the solution to a set of linear equations, expressed in matrix terms as =.
Ad
related to: linear equation solver wolfram x