  Numerous methods for computing conformal mesh paramterizations has been
developed due to the vast applications in the field of geometry processing.
Spectral conformal parameterization (SCP) is one of these methods to computing
a quality conformal parameterization based on the spectral technique. SCP focus
on a generalized eigenvalue problem (GEP) $L_{C}\mathbf{f} = \lambda
B\mathbf{f}$ whose eigenvector(s) associated with the smallest positive
eigenvalue(s) will provide the parameterization result.
  This paper devotes to study a novel eigensolver for this GEP. Based on the
structures of matrix pair $(L_{C},B)$, we show that this GEP can be transformed
into a small-scaled compressed deating standard eigenvalue problem with a
symmetric positive definite skew-Hamiltonian operator. We then propose a
skew-Hamiltonian isotropic Lanczos algorithm (SHILA) to solve the reducing
problem. Numerical experiments show that our compressed deating skill remove
the inuence of the kernel of $L_{C}$ and transform the original problem to a
more robust system. The novel SHILA method can effective avoid the disturbance
of duplicate eigenvalues. As a result, our numerical eigensolver can accurately
and efficiently compute the conformal parameterization based on the spectral
model of SCP.
