Sum of Squares

In this paper, we examine structured tensors which have sum-of-squares (SOS) tensor decomposition, and study the SOS-rank of SOS tensor decomposition. We first show that several classes of even order symmetric structured tensors available in the literature have SOS tensor decomposition. These include positive Cauchy tensors, weakly diagonally dominated tensors, B0-tensors, double B-tensors, quasi-double B0-tensors, M B0-tensors, H-tensors, absolute tensors of positive semi-definite Z-tensors and extended Z-tensors. We also examine the SOS-rank of SOS tensor decomposition and the SOS-width for SOS tensor cones. The SOS-rank provides the minimal number of squares in the SOS tensor decomposition, and, for a given SOS tensor cone, its SOS-width is the maximum possible SOS-rank for all the tensors in this cone. We first deduce an upper bound for general tensors that have SOS decomposition and the SOS-width for general SOS tensor cone using the known results in the literature of polynomial theory. Then, we provide an explicit sharper estimate for the SOS-rank of SOS tensor decomposition with bounded exponent and identify the SOS-width for the tensor cone consisting of all tensors with bounded exponent that have SOS decompositions. Finally, as applications, we show how the SOS tensor decomposition can be used to compute the minimum H-eigenvalue of an even order symmetric extended Z-tensor and test the positive definiteness of an associated multivariate form. Numerical experiments are also provided to show the efficiency of the proposed numerical methods ranging from small size to large size numerical examples.

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The Effects of Portfolio Assessment on Writing of EFL Students

Nezakatgoo¹

2011

ELT

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The primary focus of this study was to determine the effect of portfolio assessment on final examination scores of EFL students' writing skill. To determine the impact of portfolio-based writing assessment 40 university students who enrolled in composition course were initially selected and divided randomly into two experimental and control groups. A quasi-experimental research design was adopted in this study. In order to appraise the homogeneity of the experimental and control groups Comprehensive English Language Test (CELT) was employed at the beginning of the study. The pre-test was applied to both the experimental group and control group. Later in the study, a post-test of dependent variables was implemented for both groups. Data analysis was carried out by SPSS 16 statistical computer program .The statistical techniques being applied were the Levene statistic of One-Way ANOVA and the Paired-sample T-test. The results of the study revealed that that students whose work was evaluated by a portfolio system (portfolio-based assessment) had improved in their writing and gained higher scores in final examination when compared to those students whose work was evaluated by the more traditional evaluation system (non-portfolio-based assessment).The findings of the present study highlighted the fact that portfolio assessment could be used as a complementary alternative along with traditional assessment to shed new light on the process of writing.

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Sum of Squares

Abstract: We describe the notion of sums of squares, which it the leading idea behind analysis of variance. We special attention to the case of unbalanced designs, where different types of sums of squares can be used. We outline the appropriate use of these sums of squares.

Cited by 3 publications

References 10 publications

Self-calibrating Coil Sensitivity Profiles for Parallel Imaging Based on Anisotropic Diffusion

Self-calibrating Coil Sensitivity Profiles for Parallel Imaging Based on Anisotropic Diffusion

SOS tensor decomposition: Theory and applications

The Effects of Portfolio Assessment on Writing of EFL Students

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