Hermitian completions of band matrices and applications (Q1347217)

Here Hermitian completions of partial banded matrices are studied via generalized Cholesky signatures. Assuming certain nonsingularities for the band pattern for \(A\), a complete \(1-1\) description of all Hermitian completions of \(A\) with given Cholesky signature is given in terms of fractions of determinants and congruence transforms. There are corresponding results for partial \(m\)-band Toeplitz matrices and their Hermitian completion as well as efforts to achieve sparse such completions and Hermitian completions of partial triangular matrices.