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318 3. Reference Manual
A ϑ i B ˜w
ỹ H
z
ε
⩵ r
for updates z of u and v. The symbols ˜w and ỹ denote two arbitrary projection vectors, which
must be chosen appropriately in each step to ensure convergence of the iterates. Suitable choices
for ˜w and ỹ include combinations of the initial guesses and the most recent approximations of the
eigenvectors v and u.
With the option ProjectionVectors −> {wt, yt}, you can choose the vectors LREigenpair uses as
projection vectors. Possible values are:
LeftEigenvector
RightEigenvector
InitialLeftEigenvector
InitialRightEigenvector
the most recent approximation of the left eigenvector v
the most recent approximation of the right eigenvector u
the initial guess v for the left eigenvector
the initial guess u for the right eigenvector
Values for the ProjectionVectors option.
In most cases, the default setting ProjectionVectors −> {LeftEigenvector, RightEigenvector}
constitutes an appropriate choice. You will need to change the setting of this option only if you
encounter convergence problems.
Tolerance
Tolerance −> tol specifies the radius of the tolerance region around the initial guess theta0 in
which the sought eigenvalue Λ should lie. LREigenpair generates a warning if it converges to
an eigenvalue that lies outside the tolerance region. The Tolerance option allows you to check
whether LREigenpair has found the eigenvalue you wished to compute or whether the iterations
have converged to a completely different solution.
Tolerance uses a logarithmic measure for distances. For example, Tolerance −> 1.0 allows the
value of the solution Λ to lie within and times the value of the initial guess theta0.
Examples
Load Analog Insydes.
Define three square
real-valued matrices.
Solve the GEP A B
iteratively using the initial
guess theta ⩵ .
In[1]:=