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C++ API

: [aa, bb, q, z] = qzhess (A, B)

Compute the Hessenberg-triangular decomposition of the matrix pencil (A, B), returning aa = q * A * z, bb = q * B * z, with q and z orthogonal.

For example:

[aa, bb, q, z] = qzhess ([1, 2; 3, 4], [5, 6; 7, 8])
     ⇒ aa = [ -3.02244, -4.41741;  0.92998,  0.69749 ]
     ⇒ bb = [ -8.60233, -9.99730;  0.00000, -0.23250 ]
     ⇒  q = [ -0.58124, -0.81373; -0.81373,  0.58124 ]
     ⇒  z = [ 1, 0; 0, 1 ]

The Hessenberg-triangular decomposition is the first step in Moler and Stewart’s QZ decomposition algorithm.

Algorithm taken from Golub and Van Loan, Matrix Computations, 2nd edition.

See also: lu, chol, hess, qr, qz, schur, svd.

Package: octave