Class EigenBoundUtils
- java.lang.Object
-
- dev.nm.algebra.linear.matrix.doubles.factorization.eigen.mr3.EigenBoundUtils
-
public final class EigenBoundUtils extends Object
Utility methods for computing bounds of eigenvalues.
-
-
Method Summary
All Methods Static Methods Concrete Methods Modifier and Type Method Description static RealInterval[]
computeGershgorinIntervals(Vector D, Vector E)
Computes the Gershgorin bounds for all eigenvalues in a symmetric tridiagonal matrix T.static RealInterval
mergeIntervals(RealInterval[] intervals)
-
-
-
Method Detail
-
computeGershgorinIntervals
public static RealInterval[] computeGershgorinIntervals(Vector D, Vector E)
Computes the Gershgorin bounds for all eigenvalues in a symmetric tridiagonal matrix T. The Gershgorin bounds give an estimate that is wrong by at most a factor of \(\sqrt{2}\).- Parameters:
D
- the diagonal entries of TE
- the sub-diagonal entries of T- Returns:
- the eigenvalue bounds
- See Also:
- Wikipedia: Gershgorin circle theorem
-
mergeIntervals
public static RealInterval mergeIntervals(RealInterval[] intervals)
-
-