Each iteration consists of three steps: choose a suitable shift to enhance the convergence, apply a similarity transformation
to create a bulge, and chase the bulge until it disappears from the bottom of the matrix.
Therefore, in this paper, similarity transformation
methods are used to access instances before manual screening, which helps improve the efficiency of instance access greatly.
Feature matching to identify control point pairs is accomplished by defining geometric patterns which remain unchanged under a four-parameter similarity transformation
(called SIPP: Shape/ Similarity Invariant Point Pattern) and under a general six-parameter affine transformation (called AIPP: Area/Affine Invariant Point Pattern).
They developed a similarity transformation
method in which the boundary layer equation was reduced to a third-order nonlinear ordinary differential equation.
Here the solution is obtained by regarding cross-sectional velocity as perturbation parameter that has been solved by using similarity transformation
and singular perturbation technique.
These rotations are then brought by a similarity transformation
back to the left-hand side.
Unlike the affine transformation, the similarity transformation
preserves the shape of geometrical figures.
To complete the similarity transformation
, the transposed Givens transformation has to be applied to the columns; see Figure 4.
K] are easily obtained by applying a similarity transformation
to the matrix of the derivatives of the recursion coefficients, [T'.
Hence, the first step of the implicit SR step introduces a bulge by a similarity transformation
of H with
When we apply the balancing algorithm to H, it effects a diagonal similarity transformation
9] Every skew-Hamiltonian matrix is similar, via an orthogonal symplectic similarity transformation
, to a matrix in skew-Hamiltonian Schur form.