◆ Dsterf()

Eigenvalues of a symmetric tridiagonal matrix (QL or QR method)

Purpose: This routine computes all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm.

Parameters

[in]	N	Order of the matrix. (N >= 0) (If N = 0, returns without computation)
[in,out]	D()	Array D(LD - 1) (LD >= N) [in] The diagonal elements of the tridiagonal matrix. [out] If Info = 0, the eigenvalues in ascending order.
[in,out]	E()	Array E(LE - 1) (LE >= N - 1) [in] The (N-1) subdiagonal elements of the tridiagonal matrix. [out] E() has been destroyed.
[out]	Info	= 0: Successful exit. = -1: The argument N had an illegal value. (N < 0) = -2: The argument D() is invalid. = -3: The argument E() is invalid. = i > 0: The algorithm has failed to find all of the eigenvalues in a total of 30*N iterations. i elements of E() have not converged to zero.

Example Program: Compute all eigenvalues of the symmetric matrix A, where
( 2.20 -0.11 -0.32 )

A = ( -0.11 2.93 0.81 )

( -0.32 0.81 2.37 )

Reduces to tridiagonal form by Dsytrd, then Dsterf is applied.
Sub Ex_Dsytrd_Dsterf()

Const N = 3

Dim A(N - 1, N - 1) As Double, Info As Long

Dim D(N - 1) As Double, E(N - 2) As Double, Tau(N - 2) As Double

A(0, 0) = 2.2

A(1, 0) = -0.11: A(1, 1) = 2.93

A(2, 0) = -0.32: A(2, 1) = 0.81: A(2, 2) = 2.37

Call Dsytrd("L", N, A(), D(), E(), Tau(), Info)

If Info <> 0 Then

Debug.Print "Error in Dsytrd: Info =", Info

Exit Sub

End If

Call Dsterf(N, D(), E(), Info)

If Info <> 0 Then

Debug.Print "Error in Dsterf: Info =", Info

Exit Sub

End If

Debug.Print "Eigenvalues =", D(0), D(1), D(2)

End Sub

Example Results: Eigenvalues = 1.70705954911046 2.22943643244226 3.56350401844728