GNU Octave - Local Sector 7 web page

258 GNU Octaveqzval (a, b)Compute generalized eigenvalues of the matrix pencil (A − λB).a and b must be real matrices.qzval is obsolete; use qz instead.Function Filey = zgfmul (a, b, c, d, x)Function FileCompute product of zgep incidence matrix F with vector x. Used by zgepbal (inzgscal) as part of generalized conjugate gradient iteration.zgfslv (n, m, p, b)Solve system of equations for dense zgep problem.Function Filezz = zginit (a, b, c, d)Function FileConstruct right hand side vector zz for the zero-computation generalized eigenvalueproblem balancing procedure. Called by zgepbal.zgreduce (sys, meps)Function FileImplementation of procedure REDUCE in (Emami-Naeini and Van Dooren, Automatica,# 1982).[nonz, zer] = zgrownorm (mat, meps)Function FileReturn nonz = number of rows of mat whose two norm exceeds meps, and zer =number of rows of mat whose two norm is less than meps.x = zgscal (f, z, n, m, p)Function FileGeneralized conjugate gradient iteration to solve zero-computation generalized eigenvalueproblem balancing equation fx = z; called by zgepbal.[a, b] = zgsgiv (c, s, a, b)Apply givens rotation c,s to row vectors a, b.( zgpbal ); kept for backward compatibility.Function FileNo longer used in zero-balancingx = zgshsr (y)Function FileApply householder vector based on e m to column vector y. Called by zgfslv.ZGEPReferencesHodel, Computation of Zeros with Balancing, 1992, Linear Algebra and itsApplicationsGeneralized CGGolub and Van Loan, Matrix Computations, 2nd ed 1989.