<p>The matrix approximation problem with group regularization is a special structured matrix approximation and finds a variety of applications in finance, statistics, and engineering. Fast and robust algorithms for solving this important matrix approximation problem are desired in these fields. In this paper, we present a dual semismooth Newton algorithm with the guaranteed global convergence and local quadratic convergence rate. Our algorithm is based on the dual formulation with ball constraints, and by estimating the active set of the ball constraints via the active-set technique during iterations, it builds equality constrained quadratic programming subproblems and generates the generalized Newton step. To stabilize the use of the Newton step, a nonmonotone residual/objective-based strategy with the proximal gradient steps is incorporated, ensuring global convergence. Numerical results on various types of synthetic and real data sets demonstrate the efficiency and robustness of the proposed algorithm.</p>