[1] L.T. Santos
Nonlinear Systems and Fractals
"Matematica Universitaria", 15, 102-116,1993
In this work we use computer graphic techniques to analyse the
chaotic behaviour of some iterative methods for solving nonlinear
systems of dimension 2. We show the convergence regions to
illustrate the fractal geometry.
[2] J.M. Martinez, L.T. Santos and S.A. Santos
A Minimax Method with Application to the Initial Vector Coding Problem
Technical Report - Imecc - UNICAMP, RP 60/93, 1993
Submitted to "Mathematics and Computers in Simulation"
We consider the problem
Minimize max { f_1(x), f_2(x), ..., f_m(x) }
x \in S
where f_1, ...,f_m : R^n -> R are (generally nonlinear)
differentiable functions, S C R^n and n,m can be large. We introduce
a new algorithm for solving this problem that can be implemented
in rather modest computer environments. The new method is based on
a fast one-dimensional newtonian procedure applied to the
objective value of an auxiliary function. We report numerical
experiments, which suggest that the new algorithm, combined with
powerful strategy for minimization on spheres, can be an effective
tool for solving initial vector coding problems.
[3] L.T. Santos, B. Ursin and M. Tygel
Waves series Expansions for Stratified Acoustic Media
Technical Report - IMECC - UNICAMP, RP 33/94, 1994
The reflection or transmission transient response of a stack of
plane homogeneous acoustic layers between two homogeneous acoustic
half-spaces, due to a point source located in one half-space or
within the layer stack, is exactly given by an infinite superposition
of generalized waves. The main results concerning generalized waves
in time domain are reviewed. In particular, a new derivation of the
Cagniard-de Hoop expressions are obtained from the transient
Sommerfeld point-source representation in a direct manner. The
results obtained are then used to compute synthetic seismograms in a
very accurate way. Finally, asymptotic results for times close to the
main events of the propagation are derived. This derivation is also
completely done in the time domain, so that the high-frequency
assumptions made in ray-theoretical studies are not necessary.
This explain why ray theory often gives good results even when
the assumptions for its validity are violated.
[4] R.C.A. Biloti and L.T. Santos
Study of Fractals Generated by Fixed Point Iterations
Technical Report - IMECC - UNICAMP, RP 34/94, 1994
In this work we discuss the generation of fractals using fixed-point
iterations in complet spaces, whose elements are non-empty compact subsets of R^n. We review some important theorems and their
relations with the computation of the fractal dimension. We also
report one appication of this technique: the fractal interpolation.
[5] J.M. Martinez and L.T. Santos
On the Resolution of The External Penalization Problem
Technical Report - IMECC - UNICAMP, RP 40/94, 1994
Submitted to "Siam Journal on Optimization"
We introduce a nonlinear system of equations whose solution
corresponds to the minimizer of the classical quadratic penalty
function. The resolution of this system by means of Newton's method
does not have the drawbacks that are inherent to usual approaches.
We give convergence results independent of the penalty parameter
and we illustrate the theory with a numerical example.
[6] L.T. Santos and W.W. Symes
Efficient Free-Surface Kirchhoff Modeling
Technical Report - Rice University, TR95-17, 1995
The aim of this work is to introduce a new scheme to apply Kirchhoff
modeling efficiently to a 2-D acoustic model with a free surface and
with irregular source and receiver locations. We consider as data all
the traveltimes and amplitudes of each ray connecting points below
some datum depth and points over this depth. We derive a new
expression for the Kirchhoff formula which uses these computed
traveltimes and amplitudes only. Given accurate components, the
primary reflection seismograms computed via this new approach for
the Kirchhoff method is remarkably accurate and less expensive than
the usual technique. We also compare Kirchhoff seismograms with
those produced from the same model by finite-difference solution
of the linearized acoustic wave equation.
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