LinearSolveFunction
LinearSolveFunction[dimensions,data]
represents a function for providing solutions to a matrix equation.
Details
- LinearSolveFunction[…] is generated by LinearSolve[m].
- LinearSolveFunction works like Function.
- LinearSolveFunction[…][b] finds the solution to the matrix equation for the specific vector or matrix .
- dimensions specifies the dimensions of the matrix m from which the LinearSolveFunction was constructed.
Examples
open allclose allBasic Examples (1)
Scope (3)
Generalizations & Extensions (1)
Applications (2)
Find the eigenvector associated with the smallest eigenvalue:
Approximate value of the eigenvalue:
Expressions for a finite difference approximation to the Laplacian in 2 dimensions:
A matrix approximating the Laplacian operator:
A linear solve function for the matrix:
An approximate solution for the Poisson equation on the unit rectangle:
An approximate solution for the Poisson equation on the unit rectangle:
Properties & Relations (2)
A LinearSolveFunction is effectively like a matrix inverse. A large sparse matrix:
Time to compute and memory used by the linear solve function:
Time to compute and memory used by the inverse matrix:
Comparison of f and the inverse matrix for a random vector b:
Create a LinearSolveFunction for a simple matrix:
Compute the inverse matrix from f:
Compute the inverse matrix using Inverse:
Text
Wolfram Research (2003), LinearSolveFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/LinearSolveFunction.html.
CMS
Wolfram Language. 2003. "LinearSolveFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LinearSolveFunction.html.
APA
Wolfram Language. (2003). LinearSolveFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LinearSolveFunction.html