Treffer: Confluent polynomial Vandermonde-like matrices: displacement structures, inversion formulas and fast algorithm: Confluent polynomial Vandermonde-like matrices: Displacement structures, inversion formulas and fast algorithm

Three displacement operators associated with confluent polynomial Vandermonde matrices are introduced, and the classes of confluent polynomial Vandermonde-like matrices are defined. In the next section, some necessary properties for generalized Horner polynomials and for change of basis are outlined. This is followed by the derivation of two inversion formulas for confluent polynomial Vandermonde-like matrices, and the generalization of inversion formulas for simple Chebyshev Vandermonde-like matrices. The next section is devoted to the implementation of block Gaussian elimination for solving associated linear systems and fast inverse algorithm. In the following two sections, the relationship of confluent polynomial Vandermonde-like matrices with confluent Cauchy-like matrices and \(q\)-adic Vandermonde matrices on any non-algebraically closed field is described.