Trace minimization and definiteness of symmetric pencils

Trace minimization principles for positive semi-definite pencils

Article history: Received 7 September 2012 Accepted 4 December 2012 Available online 11 January 2013 Submitted by P. Šemrl AMS classification: 15A18 15A22 65F15

Pencils of Symmetric Surfaces in P 3

A Structured Staircase Algorithm for Skew-symmetric/symmetric Pencils

A STRUCTURED STAIRCASE ALGORITHM FOR SKEW-SYMMETRIC/SYMMETRIC PENCILS RALPH BYERS , VOLKER MEHRMANN , AND HONGGUO XU Abstract. We present structure preserving algorithms for the numerical computation of structured staircase forms of skew-symmetric/symmetric matrix pencils along with the Kronecker indices of the associated skew-symmetric/symmetric Kronecker-like canonical form. These methods all...

Consistency of Trace Norm Minimization

Regularization by the sum of singular values, also referred to as the trace norm, is a popular technique for estimating low rank rectangular matrices. In this paper, we extend some of the consistency results of the Lasso to provide necessary and sufficient conditions for rank consistency of trace norm minimization with the square loss. We also provide an adaptive version that is rank consistent...

On solving sparse symmetric linear systems whose definiteness is unknown

Solving a large, sparse, symmetric linear system Ax = b iteratively must use appropriate methods. The conjugate gradient (CG) method can break down if A is indefinite while algorithms such as SYMMLQ and MINRES, though stable for indefinite systems, are computationally more expensive than CG when applied to positive definite matrices. In this paper, we present an iterative method for the case wh...