Determinant of Two Types of Five-Diagonal Matrices
The value of five-diagonal determinants has very broad applications in numerical solutions of partial differential equations,image processing,circuit analysis,and bioinformatics.Firstly,in this paper,the two types of five-diagonal determinants are expanded through Laplace,and each cofactor and itself are represented as the solution of a first-order linear recursive equation system.Further,the values of the determinant are represented as the product of the power of the coefficient matrix and the initial value vector.Secondly,the values of the two types of determinants are represented as the continuous product of the solutions of the binary recursive equation system through LU decomposition.
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