slae2 (l) - Linux Manuals
slae2: computes the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]
Command to display slae2
manual in Linux: $ man l slae2
NAME
SLAE2 - computes the eigenvalues of a 2-by-2 symmetric matrix [ A B ] [ B C ]
SYNOPSIS
- SUBROUTINE SLAE2(
-
A, B, C, RT1, RT2 )
-
REAL
A, B, C, RT1, RT2
PURPOSE
SLAE2 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) REAL
-
The (1,1) element of the 2-by-2 matrix.
- B (input) REAL
-
The (1,2) and (2,1) elements of the 2-by-2 matrix.
- C (input) REAL
-
The (2,2) element of the 2-by-2 matrix.
- RT1 (output) REAL
-
The eigenvalue of larger absolute value.
- RT2 (output) REAL
-
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 slae2
- slae2 (3)
- slaebz (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
- slaed0 (l) - computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
- slaed1 (l) - computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
- slaed2 (l) - merges the two sets of eigenvalues together into a single sorted set
- slaed3 (l) - finds the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K
- slaed4 (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
- slaed5 (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
- slaed6 (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
- slaed7 (l) - computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
- slaed8 (l) - merges the two sets of eigenvalues together into a single sorted set