NAG Library Routine Document

F06BPF

+− Contents

1 Purpose

9 Example

F06BPF returns an eigenvalue of a

2

2

real symmetric matrix.

FUNCTION F06BPF (

A, B, C)

REAL (KIND=nag_wp) F06BPF

REAL (KIND=nag_wp)

A, B, C

F06BPF returns an eigenvalue of the

2

2

real symmetric matrix

(\begin{array}{r} a & b \\ b & c \end{array}),

via the function name. The result is intended for use as a shift in symmetric eigenvalue routines.

The eigenvalue is computed as

c - \frac{b}{f + sign f \times \sqrt{1 + f^{2}}},

where

f = \frac{a - c}{2 b}

This is the eigenvalue nearer to

c

a \neq c

, and is equal to

c - b

a = c

None.

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