Neural network for computing GSVD and RSVD

Abstract

This paper presents the neural dynamical network to compute the generalized and restricted singular value decompositions (GSVD/RSVD) in the regularization methods for ill-posed problems. The neural network model is defined by ordinary differential equations (ODE) which can be solved by many state-of-the-art techniques. The main purpose of the paper is to develop two neural network models for finding approximations of the GSVD and the RSVD. The globally asymptotic stability analyses are provided and numerical experiments illustrate our theory and methods. For small scale problems, the estimation can be as accurate as O(10-15). For ill-posed problems, the truncation regularization method implementing the GSVD/RSVD algorithms also produces accurate results.