CholeskyDecomposition<T> Class

public abstract class CholeskyDecomposition<T> : Decomposition<T>

Public MustInherit Class CholeskyDecomposition(Of T)
	Inherits Decomposition(Of T)

generic<typename T>
public ref class CholeskyDecomposition abstract : public Decomposition<T>

[<AbstractClassAttribute>]
type CholeskyDecomposition<'T> = 
    class
        inherit Decomposition<'T>
    end

Inheritance

Object  →  LinearOperator<T>  →  Decomposition<T>  →  CholeskyDecomposition<T>

Type Parameters

T

The Cholesky decomposition of a real symmetric positive definite matrix A rewrites the matrix in the form A= LL^T, where L is a lower-triangular matrix.

CholeskyDecomposition<T> can operate in two modes. In overwrite mode, the original matrix is overwritten with the result of the decomposition. In preserve mode, the original matrix is preserved, and a new matrix is created to hold the decomposition. You can set the mode through the Overwrite property.

CholeskyDecomposition<T> inherits from LinearOperator<T>. This means you can use it to solve systems of linear equations where the matrix of the system is symmetric and positive definite. You can solve for a single right-hand side, or for multiple right-hand sides using the Solve(Vector<T>) method. You can also calculate the determinant the inverse, and an estimate for the condition number.

To solve a general (non-symmetric or non-positive definite)system of equations, use the LUDecomposition<T> class instead.

Reference