233,829 research outputs found
Inverse spectral problem for a third-order differential operator
Inverse spectral problem for a self-adjoint differential operator, which is
the sum of the operator of the third derivative on a finite interval and of the
operator of multiplication by a real function (potential), is solved. Closed
system of integral linear equations is obtained. Via solution to this system,
the potential is calculated. It is shown that the main parameters of the
obtained system of equations are expressed via spectral data of the initial
operator. It is established that the potential is unambiguously defined by the
four spectra
Kalman filtering, smoothing and recursive robot arm forward and inverse dynamics
The inverse and forward dynamics problems for multi-link serial manipulators are solved by using recursive techniques from linear filtering and smoothing theory. The pivotal step is to cast the system dynamics and kinematics as a two-point boundary-value problem. Solution of this problem leads to filtering and smoothing techniques identical to the equations of Kalman filtering and Bryson-Frazier fixed time-interval smoothing. The solutions prescribe an inward filtering recursion to compute a sequence of constraint moments and forces followed by an outward recursion to determine a corresponding sequence of angular and linear accelerations. In addition to providing techniques to compute joint accelerations from applied joint moments (and vice versa), the report provides an approach to evaluate recursively the composite multi-link system inertia matrix and its inverse. The report lays the foundation for the potential use of filtering and smoothing techniques in robot inverse and forward dynamics and in robot control design
A linear inversion method to infer exhumation rates in space and time from thermochronometric data
We present a formal inverse procedure to extract exhumation rates from
spatially distributed low temperature thermochronometric data. Our method is
based on a Gaussian linear inversion approach in which we define a linear
problem relating exhumation rate to thermochronometric age with rates being
parameterized as variable in both space and time. The basis of our linear
forward model is the fact that the depth to the "closure isotherm" can be
described as the integral of exhumation rate, ..., from the cooling age
to the present day. For each age, a one-dimensional thermal model is used to
calculate a characteristic closure temperature, and is combined with a
spectral method to estimate the conductive effects of topography on the
underlying isotherms. This approximation to the four-dimensional thermal
problem allows us to calculate closure depths for data sets that span large
spatial regions. By discretizing the integral expressions into time intervals
we express the problem as a single linear system of equations. In addition,
we assume that exhumation rates vary smoothly in space, and so can be
described through a spatial correlation function. Therefore, exhumation rate
history is discretized over a set of time intervals, but is spatially
correlated over each time interval. We use an a priori estimate of the model
parameters in order to invert this linear system and obtain the maximum
likelihood solution for the exhumation rate history. An estimate of the
resolving power of the data is also obtained by computing the a posteriori
variance of the parameters and by analyzing the resolution matrix. The
method is applicable when data from multiple thermochronometers and
elevations/depths are available. However, it is not applicable when there
has been burial and reheating. We illustrate our inversion procedure using
examples from the literature
A time reversal based algorithm for solving initial data inverse problems
International audienceWe propose an iterative algorithm to solve initial data inverse problems for a class of linear evolution equations, including the wave, the plate, the Schr{ö}dinger and the Maxwell equations in a bounded domain . We assume that the only available information is a distributed observation (i.e. partial observation of the solution on a sub-domain during a finite time interval ). Under some quite natural assumptions (essentially : the exact observability of the system for some time , and the existence of a time-reversal operator for the problem), an iterative algorithm based on a Neumann series expansion is proposed. Numerical examples are presented to show the efficiency of the method
An Overview of Polynomially Computable Characteristics of Special Interval Matrices
It is well known that many problems in interval computation are intractable,
which restricts our attempts to solve large problems in reasonable time. This
does not mean, however, that all problems are computationally hard. Identifying
polynomially solvable classes thus belongs to important current trends. The
purpose of this paper is to review some of such classes. In particular, we
focus on several special interval matrices and investigate their convenient
properties. We consider tridiagonal matrices, {M,H,P,B}-matrices, inverse
M-matrices, inverse nonnegative matrices, nonnegative matrices, totally
positive matrices and some others. We focus in particular on computing the
range of the determinant, eigenvalues, singular values, and selected norms.
Whenever possible, we state also formulae for determining the inverse matrix
and the hull of the solution set of an interval system of linear equations. We
survey not only the known facts, but we present some new views as well
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