Abstract. An efficient method for the computation to high relative accuracy of the LDU decomposition of an n × n row diagonally dominant M -matrix is presented, assuming that the off-diagonal entries and row sums are given. This method costs an additional O(n 2 ) elementary operations over the cost of Gaussian elimination, and leads to a lower triangular, column diagonally dominant matrix and an upper triangular, row diagonally dominant matrix. Comparisons with other methods in the literature are commented and illustrated.

A class of sign-symmetric P -matrices including all nonsingular totally positive matrices and their inverses as well as tridiagonal nonsingular H -matrices is presented and analyzed. These matrices present a bidiagonal decomposition that can be used to obtain algorithms to compute with high relative accuracy their singular values, eigenvalues, inverses, or their LDU factorization.

The aim of this research is to determine the impact of perceived Teachers’ Digital Competence (TDC) on how well math teachers prepare the educational videos needed to put the flipped classroom model into practice. In preparing the videos, the teachers had to select pre-existing audiovisual material and then edit the content to adapt it to the flipped classroom. Described here is a non-experimental study of a sample of 50 teachers pursuing a Master’s degree in Secondary School Math Education in Spain. This is a preliminary univariate descriptive study of the relationship between TDC and the quality of videos prepared. Possible correlations between these two variables and between the characteristics of the sample are also explored. In general, the teachers had an intermediate level of TDC and prepared satisfactory videos. Nevertheless, the videos were deficient in the sections related to their pedagogical and math instructional components. No correlation was observed between TDC and the quality of the videos prepared. These results indicate that the integration of technological, pedagogical, and math instructional components is more important for developing quality instructional videos than the technological component alone. Teacher training should incorporate elements which emphasize the application of technology to the pedagogical process of math instruction.

Abstract. Matrices, called ε-BD matrices, that have a bidiagonal decomposition satisfying some sign constraints are analyzed. The ε-BD matrices include all nonsingular totally positive matrices, as well as their matrices opposite in sign and their inverses. The signs of minors of ε-BD matrices are analyzed. The zero patterns of ε-BD matrices and their triangular factors are studied and applied to prove the backward stability of Gaussian elimination without pivoting for the associated linear systems.

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