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Approximating spectral densities of large matrices
In physics, it is sometimes desirable to compute the so-called \emph{Density
Of States} (DOS), also known as the \emph{spectral density}, of a real
symmetric matrix . The spectral density can be viewed as a probability
density distribution that measures the likelihood of finding eigenvalues near
some point on the real line. The most straightforward way to obtain this
density is to compute all eigenvalues of . But this approach is generally
costly and wasteful, especially for matrices of large dimension. There exists
alternative methods that allow us to estimate the spectral density function at
much lower cost. The major computational cost of these methods is in
multiplying with a number of vectors, which makes them appealing for
large-scale problems where products of the matrix with arbitrary vectors
are relatively inexpensive. This paper defines the problem of estimating the
spectral density carefully, and discusses how to measure the accuracy of an
approximate spectral density. It then surveys a few known methods for
estimating the spectral density, and proposes some new variations of existing
methods. All methods are discussed from a numerical linear algebra point of
view
New high fill-factor triangular micro-lens array fabrication method using UV proximity printing
A simple and effective method to fabricate a high fill-factor triangular
microlens array using the proximity printing in lithography process is
reported. The technology utilizes the UV proximity printing by controlling a
printing gap between the mask and substrate. The designed approximate triangle
microlens array pattern can be fabricated the high fill-factor triangular
microlens array in photoresist. It is due to the UV light diffraction to
deflect away from the aperture edges and produce a certain exposure in
photoresist material outside the aperture edges. This method can precisely
control the geometric profile of high fill factor triangular microlens array.
The experimental results showed that the triangular micro-lens array in
photoresist could be formed automatically when the printing gap ranged from 240
micrometers to 840 micrometers. The gapless triangular microlens array will be
used to increases of luminance for backlight module of liquid crystal displays.Comment: Submitted on behalf of EDA Publishing Association
(http://irevues.inist.fr/handle/2042/16838
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