Reliability Analysis of Sports Training Evaluation Index Based on Random Matrix

Abstract

This paper presents an in-depth study and analysis of the reliability of indicators for the evaluation of sports training using the algorithm of random matrices. Random matrix theory is used to obtain the degree of randomness of the data and the overall correlation characteristics of the data through statistical analysis of the energy spectrum and eigenstates of complex systems. Using the results of random matrix theory on the eigenvalues of the sample covariance matrix, the energy of each subspace is estimated, and the estimated energy is then used to construct the subspace weighting matrix. The problem of reliable finite-time stability of the model under several types of uncertain time-lagged bounded transfer probability Markov jump parameter compatibility indicators is also explored. The four basic theoretical issues, namely, value orientation, construction basis, construction principles, and conceptual model of the sports training work evaluation index system, are studied. This paper takes the construction of a sports training evaluation index system as the research object and uses the literature method, expert interview method, questionnaire survey method, data analysis method, Delphi method, and hierarchical analysis method as the main research methods to construct a set of sports training evaluation index system as the research task, to enrich the idea of sports training evaluation work, and to provide a reference for the future government to be able to develop a sports training evaluation index system that is in line with the development of the times. The research method was used to collect the opinions of experts. The subjective opinions given by experts were collected using the assignment method, and the weight coefficients of each index were calculated using the AHP hierarchical analysis method. The result is that the index of basic conditions (0.3591) has the largest weight in the whole system. After that, organization and management (0.1911), work effectiveness (0.1376), staffing (0.103), activity development (0.0828), financial and fund management (0.0562), publicity and reporting (0.0382), and material provision (0.032) are in order. The evaluation results of the index system are consistent with the current actual situation of specialization teaching, indicating that the index system for evaluating the effectiveness of high school sports training has good validity.