The paper introduces the UTV decomposition of dual matrices (DUTV) as an efficient method for large-scale low-rank approximation. Dual numbers, which have the form $ a + b\epsilon $, are used to represent infinitesimal perturbations or time derivatives. The DUTV method provides an explicit expression and necessary conditions for the existence of dual matrix decomposition. It is shown that the general low-rank model for dual matrices can be solved via the Sylvester equation. Numerical experiments demonstrate that DUTV outperforms the dual matrix SVD algorithm in speed and maintains effectiveness in wave recognition. The DUTV algorithm is applied to validate brain functional circuits in large-scale task-state functional magnetic resonance imaging (fMRI) data, successfully identifying three types of wave signals. This provides empirical evidence for cognitive neuroscience theories. Dual matrices have been studied in various fields, including robotics, computer graphics, control theory, optimization, and differential equations. Previous studies have focused on specific dual matrix structures, such as SVD and QR decompositions. However, these methods face computational challenges with large-scale data. The DUTV algorithm is proposed as a more efficient alternative to the compact dual singular value decomposition (CDSVD). It is shown that the existence problem in DUTV can be transformed into two matrix equations satisfying the Sylvester equation. The DUTV algorithm is efficient, stable, and suitable for large-scale data. It is particularly effective in wave identification and has strong generalization capabilities. In large-scale fMRI data, the DUTV algorithm performs well in verifying classic functional brain circuits. The paper is structured with sections on dual number operations, the UTV decomposition, and the derivation of the DUTV algorithm.The paper introduces the UTV decomposition of dual matrices (DUTV) as an efficient method for large-scale low-rank approximation. Dual numbers, which have the form $ a + b\epsilon $, are used to represent infinitesimal perturbations or time derivatives. The DUTV method provides an explicit expression and necessary conditions for the existence of dual matrix decomposition. It is shown that the general low-rank model for dual matrices can be solved via the Sylvester equation. Numerical experiments demonstrate that DUTV outperforms the dual matrix SVD algorithm in speed and maintains effectiveness in wave recognition. The DUTV algorithm is applied to validate brain functional circuits in large-scale task-state functional magnetic resonance imaging (fMRI) data, successfully identifying three types of wave signals. This provides empirical evidence for cognitive neuroscience theories. Dual matrices have been studied in various fields, including robotics, computer graphics, control theory, optimization, and differential equations. Previous studies have focused on specific dual matrix structures, such as SVD and QR decompositions. However, these methods face computational challenges with large-scale data. The DUTV algorithm is proposed as a more efficient alternative to the compact dual singular value decomposition (CDSVD). It is shown that the existence problem in DUTV can be transformed into two matrix equations satisfying the Sylvester equation. The DUTV algorithm is efficient, stable, and suitable for large-scale data. It is particularly effective in wave identification and has strong generalization capabilities. In large-scale fMRI data, the DUTV algorithm performs well in verifying classic functional brain circuits. The paper is structured with sections on dual number operations, the UTV decomposition, and the derivation of the DUTV algorithm.