Exploration of Calculation Methods for a Class of Sparse Determinants

Claw-shaped determinants, as a type of sparse determinant, have extensive applications in various fields such as matrix theory, numerical computation, physics, engineering, economics, and computer science. To efficiently compute the values of claw-shaped determinants, this paper first categorizes them into four types. Next, using the properties of determinants, the calculation formulas for these four types of claw-shaped determinants are discussed. Finally, numerical examples demonstrate the rationality of these formulas.