F06 Chapter Contents
F06 Chapter Introduction
NAG Library Manual

# NAG Library Routine DocumentF06BPF

Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

## 1  Purpose

F06BPF returns an eigenvalue of a $2$ by $2$ real symmetric matrix.

## 2  Specification

 FUNCTION F06BPF ( A, B, C)
 REAL (KIND=nag_wp) F06BPF
 REAL (KIND=nag_wp) A, B, C

## 3  Description

F06BPF returns an eigenvalue of the $2$ by $2$ real symmetric matrix
 $a b b c ,$
via the function name. The result is intended for use as a shift in symmetric eigenvalue routines.
The eigenvalue is computed as
 $c - b f + sign⁡f × 1+f2 ,$
where $f=\frac{a-c}{2b}$.
This is the eigenvalue nearer to $c$ if $a\ne c$, and is equal to $c-b$ if $a=c$.

None.

## 5  Parameters

1:     A – REAL (KIND=nag_wp)Input
On entry: the value $a$, the $\left(1,1\right)$ element of the input matrix.
2:     B – REAL (KIND=nag_wp)Input
On entry: the value $b$, the $\left(1,2\right)$ or $\left(2,1\right)$ element of the input matrix.
3:     C – REAL (KIND=nag_wp)Input
On entry: the value $c$, the $\left(2,2\right)$ element of the input matrix.

None.

Not applicable.