In this study, improved algorithms based on kernel norm minimization are proposed, namely, standard CUR decomposition and fast CUR decomposition. The CUR decomposition algorithm is to decompose the matrix into three parts, namely, C, U, and R. The matrices C and R are sampled by the column selection algorithm, and then, matrix inversion and matrix multiplication are performed to obtain the cross-matrix U. The matrix C ∗ U ∗ R is an approximation of the original matrix. For the improvement of the singular value algorithm, two random algorithms are proposed, namely, the standard random k-SVD algorithm and the fast random k-SVD algorithm. The main idea is to perform dimensionality reduction and random sampling on the original large-scale data matrix, use the random projection algorithm to obtain an approximation of the original data matrix, then, perform corresponding matrix operations on this approximate matrix, and finally obtain a result similar to the original matrix calculation. Based on the empirical investigation of the current situation of physical education teaching evaluation in a university, this research conducts a questionnaire survey on the student group. Combined with the classification of various majors, the relevant factors of the physical education teaching evaluation system are analyzed and studied, and a more reasonable and unique evaluation model is established. We analyze the dimensions and content of the evaluation index system of physical education, and determine the indicators and weights. From the perspective of the combination of physical education curriculum reform and professional characteristics in a university, this study analyzes the current situation of physical education teaching evaluation and builds a sports teaching evaluation system, so as to deepen the reform of physical education teaching in colleges and universities and create a sports education system with higher vocational characteristics. The teaching evaluation model has certain practical significance.