The invention discloses an ill-conditioned matrix SVD
decomposition preprocessing method and device based on
deep learning, and a medium, and belongs to the technical field of numerical algebra and
deep learning. The method comprises the following steps: constructing an iterative deep
neural network learning framework, extracting matrix features by using a convolutional layer, and constructing an
orthogonal matrix through a House holder reflection
decomposition method; training the network by using a mixed
loss function, forcing the network to output an approximate
diagonal matrix by punishing off-
diagonal elements, and performing multiple rounds of iterative optimization by taking a learning result as the input of a new round of training; a
precondition is constructed based on a matrix obtained through training, an original ill-conditioned linear equation set is preprocessed, and a preconditioned equation set is solved through an iterative
algorithm. The method can be adapted to an ill-conditioned
general matrix without a special structure, effectively solves the problems of insufficient approximation precision and poor generalization ability of a traditional method, and remarkably improves the
numerical stability, convergence efficiency and calculation precision of high-dimensional ill-conditioned
matrix solution.