10,101 research outputs found
Quadratic Approximation of Generalized Tribonacci Sequences
In this paper, we give quadratic approximation of generalized Tribonacci
sequence defined by Eq. (\ref{eq:7}) and use this result
to give the matrix form of the -th power of a companion matrix of
. Then we re-prove the cubic identity or Cassini-type
formula for and the Binet's formula of the generalized
Tribonacci quaternions.Comment: 10 page
On Linear Quadratic Approximations
We prove the generality of the methodology proposed in Benigno and Woodford (2006). We show that, even in the presence of a distorted steady state, it is always possible and relatively simple to obtain a purely quadratic approximation to the welfare measure. We also show that, in order to do so, the timeless perspective assumption is crucial.Linear-Quadratic Approximation; Distorted Steady State; Timeless Perspective
Linear-Quadratic Approximation of Optimal Policy Problems
We consider a general class of nonlinear optimal policy problems involving forward-looking constraints (such as the Euler equations that are typically present as structural equations in DSGE models), and show that it is possible, under regularity conditions that are straightforward to check, to derive a problem with linear constraints and a quadratic objective that approximates the exact problem. The LQ approximate problem is computationally simple to solve, even in the case of moderately large state spaces and flexibly parameterized disturbance processes, and its solution represents a local linear approximation to the optimal policy for the exact model in the case that stochastic disturbances are small enough. We derive the second-order conditions that must be satisfied in order for the LQ problem to have a solution, and show that these are stronger, in general, than those required for LQ problems without forward-looking constraints. We also show how the same linear approximations to the model structural equations and quadratic approximation to the exact welfare measure can be used to correctly rank alternative simple policy rules, again in the case of small enough shocks.
Linear-Quadratic Approximation, Efficiency and Target-Implementability
We examine linear-quadratic (LQ) approximation of stochastic dynamic optimization problems in macroeconomics (and elsewhere), in particular in policy analysis using Dynamic Stochastic General Equilibrium (DSGE) models. We first define the problem that is solved by a social planner, given that the objective of the latter is to maximize average welfare; this yields the efficient solution. We then comment on the LQ approximation when a tax or subsidy can be imposed such that the zero-inflation competitive steady state output level is equal to the efficient level. We then examine the correct procedure for replacing a stochastic non-linear dynamic optimization problem with a linear-quadratic approximation. We show that a procedure proposed by Benigno and Woodford (2004) for large underlying distortions in the economy can be more easily implemented through a second-order approximation of the Hamiltonian used to compute the ex ante optimal policy with commitment (the Ramsey problem). We then define the notion of Target-Implementability, which is also a sufficient condition for a particular steady-state maximum of the Ramsey problem, and explain the usefulness of this in the context of stabilization policyLinear-quadratic approximation, dynamic stochastic general equilibrium models, utility-based loss function
Camera motion estimation through planar deformation determination
In this paper, we propose a global method for estimating the motion of a
camera which films a static scene. Our approach is direct, fast and robust, and
deals with adjacent frames of a sequence. It is based on a quadratic
approximation of the deformation between two images, in the case of a scene
with constant depth in the camera coordinate system. This condition is very
restrictive but we show that provided translation and depth inverse variations
are small enough, the error on optical flow involved by the approximation of
depths by a constant is small. In this context, we propose a new model of
camera motion, that allows to separate the image deformation in a similarity
and a ``purely'' projective application, due to change of optical axis
direction. This model leads to a quadratic approximation of image deformation
that we estimate with an M-estimator; we can immediatly deduce camera motion
parameters.Comment: 21 pages, version modifi\'ee accept\'e le 20 mars 200
Resolvent estimates for non-selfadjoint operators with double characteristics
We study resolvent estimates for non-selfadjoint semiclassical
pseudodifferential operators with double characteristics. Assuming that the
quadratic approximation along the double characteristics is elliptic, we obtain
polynomial upper bounds on the resolvent in a suitable region inside the
pseudospectrum.Comment: 38 pages. J. London Math. Soc., to appear. Published version may
diffe
An algorithm for the quadratic approximation
The quadratic approximation is a three dimensional analogue of the two dimensional Pade approximation. A determinantal expression
for the polynomial coefficients of the quadratic approximation is
given. A recursive algorithm for the construction of these coefficients
is derived. The algorithm constructs a table of quadratic
approximations analogous to the Pade table of rational approximations
An algorithm for the quadratic approximation
The quadratic approximation is a three dimensional analogue of the two dimensional Pade approximation. A determinantal expression
for the polynomial coefficients of the quadratic approximation is
given. A recursive algorithm for the construction of these coefficients
is derived. The algorithm constructs a table of quadratic
approximations analogous to the Pade table of rational approximations
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