Package dev.nm.algebra.linear.matrix.doubles.factorization.eigen.mr3

Class Summary

Class	Description
BlockSplitPointSearch	Computes the splitting points with the given threshold.
EigenBoundUtils	Utility methods for computing bounds of eigenvalues.
EigenCount	Counts the number of eigenvalues in a symmetric tridiagonal matrix T that are less than a given value x.
EigenCountInRange	Finds the number of eigenvalues of the symmetric tridiagonal matrix T that are in a given interval.
LDDecomposition	Represents a \(L D L^{\mathsf T}\) decomposition of a shifted symmetric tridiagonal matrix T.
LDFactorizationFromRoot	Decomposes (T - σ I) into \(L D L^{\mathsf T}\) where T is a symmetric tridiagonal matrix, σ is a shift for this factorization, L is a unit lower triangular matrix, and D is a diagonal matrix.
MR3	Computes eigenvalues and eigenvectors of a given symmetric tridiagonal matrix T using "Algorithm of Multiple Relatively Robust Representations" (MRRR).
SturmCount	Computes the Sturm count, the number of negative pivots encountered while factoring tridiagonal \(T - \sigma I = LDL^{\mathsf T}\).
SymmetricEigenByMR3	Computes eigen decomposition for a symmetric matrix using "Algorithm of Multiple Relatively Robust Representations" (MRRR).
SymmetricEigenFor2x2Matrix	Computes the eigen decomposition of a 2-by-2 symmetric matrix in the following form by symmetric QR algorithm. \[ \begin{bmatrix} a & b\\ b & c \end{bmatrix} \]