An efficient method for the split quaternion equality constrained least squares problem in split quaternionic mechanics

In the theoretical explorations and numerical computations of split quaternionic mechanics, a common extremely effective tool for study quantum mechanics field theory is quaternion equality constrained least squares (LSESQ) problem. This paper first time studies generalized singular value decomposition matrices (GSVDSQ) based on $$2\times 2$$ isomorphic representation obtains GSVDSQ theorem. addition, this proves necessary sufficient conditions LSESQ problem to have solutions gives an efficient method solving Finally, two examples are presented demonstrate efficiency proposed method.