Fixed-precision randomized quaternion singular value decomposition algorithm for low-rank quaternion matrix approximations

Abstract

The fixed-precision randomized quaternion singular value decomposition algorithm (FPRQSVD) is presented to compute the low-rank quaternion matrix approximation. The FPRQSVD algorithm estimates the appropriate rank according to the given tolerance without a predetermined rank parameter, and computes the corresponding low-rank quaternion matrix approximation automatically. Error analysis indicates that the FPRQSVD algorithm is mathematically equivalent to the randomized quaternion singular value decomposition algorithm. Numerical experiments are given to demonstrate that the FPRQSVD algorithm is feasible and effective. Moreover, we use it to deal with the problem of color image inpainting.