On the characterization of almost strictly sign regular matrices

Almost strictly totally negative matrices: An algorithmic characterization

“…The backward identity matrix allows us relating the signatures of an ASSR matrix A and P n A by means of the following result (see [11]). …”

“…In this work the authors deal with another subset of ASSR matrices called Almost Strictly Totally Negative (ASTN). All nontrivial minor of these matrices are strictly negative, which notably simplifies the characterization proposed in [11] for ASSR matrices. ASTN matrices form an intermediate class of matrices between TN and STN matrices.…”

“…It contains the class of Almost Strictly Totally Positive (ASTP) matrices (see [10]). ASSR matrices were characterized through the Neville Elimination (NE) in [11]. In this work the authors deal with another subset of ASSR matrices called Almost Strictly Totally Negative (ASTN).…”

Comparing pivoting strategies for almost strictly sign regular matrices

“…, n(n − 1)/2 − 1, Q t is the permutation matrix of the corresponding step of (8) and L t is the corresponding E i (α) obtained from (9). Note that if NE without pivoting is considered then the growth factor is denoted by g N E (A) and can be defined as in (10) but taking into account that…”

“…The goal of this work is the study of another subclass of SR matrices: the almost strictly sign regular (ASSR) matrices (see [10]). These matrices have all their nontrivial minors of the same order with the same strict sign and this subclass contains the nonsingular almost strictly totally positive (ASTP) matrices, introduced by Gasca, Miccheli and Peña (see [11]).…”