Lipschitzian solutions to linear iterative equations revisited

Iterative Solutions to Some Linear Matrix Equations

In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F ; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = X ; (d) AXB+CY D = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be ob...

Implicit solutions to some Lorentz invariant non-linear equations revisited

An implicit solution to the vanishing of the so-called Universal Field Equation, or Bordered Hessian, which dates at least as far back as 1935 [1] is revived, and derived from a much later form of the solution. A linear ansatz for an implicit solution of second order partial differential equations, previously shown to have wide applicability [2] is at the heart of the Chaundy solution, and is s...

m-Fold Hypergeometric Solutions of Linear Recurrence Equations Revisited

We present two algorithms to compute m-fold hypergeometric solutions of linear recurrence equations for the classical shift case and for the q-case, respectively. The first is an m-fold generalization and q-generalization of the algorithm by van Hoeij (1998a), Cluzeau and van Hoeij (2005) for recurrence equations. The second is a combination of an improved version of the algorithms by Petkovšek...

Iterative solutions to the linear matrix equation

In this paper the gradient based iterative algorithm is presented to solve the linear matrix equation AXB +CXD = E, where X is unknown matrix, A,B,C,D,E are the given constant matrices. It is proved that if the equation has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. Two numerical examples show that the introduced iterative a...

Minimal periods of periodic solutions of some Lipschitzian differential equations