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Factorizations and Reductions of Order in Quadratic and other Non-recursive Higher Order Difference Equations
non-recursive form symmetry factorization semi-invertible map criterion
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2010/12/28
A higher order difference equation may be generally defined in an arbitrary nonempty set S as:
fn(xn, xn−1, . . . , xn−k) = gn(xn, xn−1, . . . , xn−k)where fn, gn: Sk+1→ S are...
Higher order Painleve system of type D^{(1)}_{2n+2} and monodromy preserving deformation
Painleve system monodromy preserving deformation
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2010/11/8
The higher order Painleve system of type D^{(1)}_{2n+2} is proposed by Y. Sasano. It is an extension of the sixth Painleve equation for the affine Weyl group symmetry and expressed as a Hamiltonian sy...
Higher-order derivatives of the QR and of the real symmetric eigenvalue decomposition in forward and reverse mode algorithmic differentiation
univariate Taylor polynomial arithmetic higher-order derivatives QR decomposition real symmetric eigenvalue decomposition
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2010/12/15
We address the task of higher-order derivative evaluation of computer programs that contain QR
decompositions and real symmetric eigenvalue decompositions. The approach is a combination of univariate...
PRECONDITIONING HIGHER ORDER FINITE ELEMENTSYSTEMS BY ALGEBRAICMULTIGRID METHOD OF LINEAR ELEMENTS
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2007/12/12
We present and analyze a robust preconditioned conjugate gradient
method for the higher order Lagrangian finite element systems of
a class of elliptic problems. An auxiliary linear element
stiffnes...
On the Unique Continuation Property for the Higher Order Nonlinear Schrödinger Equation With Constant Coefficients
Higher order nonlinear Schrö dinger equation unique continuation property
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2010/2/26
We solve the unique continuation property: If u is a solution of the higher order nonlinear Schrödinger equation with constant coefficients with t1 < t2 which is sufficiently smooth and such that...