This paper introduces an efficient approach for handling large-scale data low-rank approximation problems using the UTV decomposition of dual matrices (DUTV). The authors propose an explicit expression for the DUTV and provide necessary and sufficient conditions for its existence. They also discover that the general low-rank model for dual matrices can be solved using the Sylvester equation. Numerical experiments show that the DUTV algorithm outperforms the dual matrix SVD algorithm in terms of speed and maintains effective performance in wave recognition. The DUTV algorithm is then applied to validate brain functional circuits in large-scale task-state functional magnetic resonance imaging (fMRI) data, successfully identifying three types of wave signals and providing substantial empirical evidence for cognitive neuroscience theories. The paper is structured into sections covering the introduction, operational rules and notations for dual numbers, the UTV decomposition, and the Sylvester equation, as well as the derivation and application of the DUTV algorithm.This paper introduces an efficient approach for handling large-scale data low-rank approximation problems using the UTV decomposition of dual matrices (DUTV). The authors propose an explicit expression for the DUTV and provide necessary and sufficient conditions for its existence. They also discover that the general low-rank model for dual matrices can be solved using the Sylvester equation. Numerical experiments show that the DUTV algorithm outperforms the dual matrix SVD algorithm in terms of speed and maintains effective performance in wave recognition. The DUTV algorithm is then applied to validate brain functional circuits in large-scale task-state functional magnetic resonance imaging (fMRI) data, successfully identifying three types of wave signals and providing substantial empirical evidence for cognitive neuroscience theories. The paper is structured into sections covering the introduction, operational rules and notations for dual numbers, the UTV decomposition, and the Sylvester equation, as well as the derivation and application of the DUTV algorithm.