---
name: "slae2"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/slae2/3lapack"
---

# slae2(3lapack)

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

## 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.\