Module ojalgo
Package org.ojalgo.matrix.decomposition

Interface Cholesky<N extends Comparable<N>>

All Superinterfaces:
DeterminantTask<N>, InverterTask<N>, InvertibleFactor<N>, LDU<N>, MatrixDecomposition<N>, MatrixDecomposition.Determinant<N>, MatrixDecomposition.Hermitian<N>, MatrixDecomposition.Ordered<N>, MatrixDecomposition.RankRevealing<N>, MatrixDecomposition.Solver<N>, MatrixTask<N>, Provider2D, Provider2D.Determinant<N>, Provider2D.Inverse<Optional<MatrixStore<N>>>, Provider2D.Rank, Provider2D.Solution<Optional<MatrixStore<N>>>, SolverTask<N>, Structure1D, Structure2D
All Known Implementing Classes:
DenseCholesky, DenseCholesky.C128, DenseCholesky.H256, DenseCholesky.Q128, DenseCholesky.R064, DenseCholesky.R128, RawCholesky
public interface Cholesky<N extends Comparable<N>> extends LDU<N>, MatrixDecomposition.Hermitian<N>

Cholesky: [A] = [L][L]H (or [R]H[R])

[A]H = [A] = [L][L]H

If [A] is symmetric and positive definite then the general LU decomposition - [P][L][D][U] - becomes [I][L][D][L]T (or [I][U]T[D][U]). [I] can be left out and [D] is normally split in halves and merged with [L] (and/or [U]). We'll express it as [A] = [L][L]T.

A cholesky decomposition is still/also an LU decomposition where [P][L][D][U] => [L][L]T.