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Presently, the teaching of interior design in most higher education institutions still uses more traditional and conservative teaching methods, which to some extent, hinders the reform of interior design teaching in the era of big data. Interior design originally required students to grasp the operation fully and use CAD, 3D, and other design software, which makes the operation of complex commands, and model construction diversity, difficult for students to learn. This situation still uses the traditional lecture-based indoctrination teaching can play a very small role. This paper first focuses on the field of interior design education, based on the background of the times, provides a deep overview of the current situation of the relevant research involved in interior design, and explains the purpose, ideas, content, and methods of this paper. Secondly, we use data mining technology to build a smart classroom to visually present interior design. Finally, a comparison experiment between the traditional teaching mode of interior design and the smart teaching mode of big data is carried out, and three groups of experimental subjects are investigated after nearly one month of teaching experience. The results of this study show that the big data wisdom teaching model proposed in this paper compared with the traditional teaching model, through the one-month teaching experience post-test results, the average increase of 7 points in school A, 11 points in school K, and 14 points in school Z. The wisdom teaching system based on big data built in this paper enhanced the relevance and initiative of interior design students’ learning, improved students’ interest in learning and classroom efficiency and promoted students’ comprehensive ability while playing a positive and active role.

The arrival of the era of big data and integrated media has changed the way of media communication and broken the original single media narrative model. The interaction and communication between traditional media and emerging media have formed a new paradigm of narrative, i.e., cross-media narrative. Based on the purpose of studying the cross-media narrative ability cultivation system of screenwriting art talents, this paper analyzes the market growth of cross-media narrative works in the era of integrated media and the audience’s perceptions of cross-media narrative works such as IP adaptations using the K-means clustering method. From 2018 to 2021, the market share of cross-media narrative works grew from 21.1% to 35.3%, while traditional single-media narrative works declined by 34.76%. Faced with the surge of transmedia narrative works, 29.5% of viewers think the stories are unattractive, too homogeneous, and lack freshness. Another 24.6% of viewers think that the plot lacks originality and only copies novels. Another 33.2% of viewers think there is plagiarism and piracy. The current cross-media narrative works still have many problems, such as rough production and a lack of polished plots. The education of film and television scriptwriting should focus on the cultivation of cross-media narrative quality, the enhancement of cross-media narrative ability, and the training of cross-media narrative skills for scriptwriting talents to cultivate high-level applied scriptwriting talents who can connect with the industry.

We propose and analyze a new spectral collocation method to solve eigenvalue problems of compact integral operators, particularly, piecewise smooth operator kernels and weakly singular operator kernels of the form 1/|t − s|μ, 0 < μ < 1. We prove that the convergence rate of eigenvalue approximation depends upon the smoothness of the corresponding eigenfunctions for piecewise smooth kernels. On the other hand, we can numerically obtain a higher rate of convergence for the above weakly singular kernel for some μ's even if the eigenfunction is not smooth. Numerical experiments confirm our theoretical results.