dlae2 (l) - Linux Manuals

dlae2: computes the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]

NAME

DLAE2 - computes the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]

SYNOPSIS

SUBROUTINE DLAE2(
A, B, C, RT1, RT2 )

    
DOUBLE PRECISION A, B, C, RT1, RT2

PURPOSE

DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix
[  A   B  ]
[  B   C  ]. On return, RT1 is the eigenvalue of larger absolute value, and RT2 is the eigenvalue of smaller absolute value.

ARGUMENTS

A (input) DOUBLE PRECISION
The (1,1) element of the 2-by-2 matrix.
B (input) DOUBLE PRECISION
The (1,2) and (2,1) elements of the 2-by-2 matrix.
C (input) DOUBLE PRECISION
The (2,2) element of the 2-by-2 matrix.
RT1 (output) DOUBLE PRECISION
The eigenvalue of larger absolute value.
RT2 (output) DOUBLE PRECISION
The eigenvalue of smaller absolute value.

FURTHER DETAILS

RT1 is accurate to a few ulps barring over/underflow.
RT2 may be inaccurate if there is massive cancellation in the determinant A*C-B*B; higher precision or correctly rounded or correctly truncated arithmetic would be needed to compute RT2 accurately in all cases.
Overflow is possible only if RT1 is within a factor of 5 of overflow. Underflow is harmless if the input data is 0 or exceeds

underflow_threshold / macheps.

Pages related to dlae2

  • dlae2 (3)
  • dlaebz (l) - contains the iteration loops which compute and use the function N(w), which is the count of eigenvalues of a symmetric tridiagonal matrix T less than or equal to its argument w
  • dlaed0 (l) - computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
  • dlaed1 (l) - computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
  • dlaed2 (l) - merges the two sets of eigenvalues together into a single sorted set
  • dlaed3 (l) - finds the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K
  • dlaed4 (l) - subroutine compute the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0
  • dlaed5 (l) - subroutine compute the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j
  • dlaed6 (l) - computes the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true
  • dlaed7 (l) - computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
  • dlaed8 (l) - merges the two sets of eigenvalues together into a single sorted set