DEMO_COND demonstrates the role of the condition
number of a matrix (with respect to inversion)
in the role of linear system solving.
Matthias Heinkenschloss
Department of Computational and Applied Mathematics
Rice University
Feb 22, 2001
This book has been written to support a practically oriented course in programming language
translation for senior undergraduates in Computer Science. More specifically, it is aimed at students
who are probably quite competent in the art of imperative programming (for example, in C++,
Pascal, or Modula-2), but whose Mathematics may be a little weak students who require only a
solid introduction to the subject, so as to provide them with insight into areas of language design
and implementation, rather than a deluge of theory which they will probably never use again
students who will enjoy fairly extensive case studies of translators for the sorts of languages with
which they are most familiar students who need to be made aware of compiler writing tools, and to
come to appreciate and know how to use them. It will hopefully also appeal to a certain class of
hobbyist who wishes to know more about how translators work.
matlab有限元網(wǎng)格劃分程序
DistMesh is a simple MATLAB code for generation of unstructured triangular and tetrahedral meshes. It was developed by Per-Olof Persson (now at UC Berkeley) and Gilbert Strang in the Department of Mathematics at MIT. A detailed description of the program is provided in our SIAM Review paper, see documentation below.
One reason that the code is short and simple is that the geometries are specified by Signed Distance Functions. These give the shortest distance from any point in space to the boundary of the domain. The sign is negative inside the region and positive outside. A simple example is the unit circle in 2-D, which has the distance function d=r-1, where r is the distance from the origin. For more complicated geometries the distance function can be computed by interpolation between values on a grid, a common representation for level set methods.
For the actual mesh generation, DistMesh uses the Delaunay triangulation routine in MATLAB and tries to optimize the node locations by a force-based smoothing procedure. The topology is regularly updated by Delaunay. The boundary points are only allowed to move tangentially to the boundary by projections using the distance function. This iterative procedure typically results in very well-shaped meshes.
Our aim with this code is simplicity, so that everyone can understand the code and modify it according to their needs. The code is not entirely robust (that is, it might not terminate and return a well-shaped mesh), and it is relatively slow. However, our current research shows that these issues can be resolved in an optimized C++ code, and we believe our simple MATLAB code is important for demonstration of the underlying principles.
To use the code, simply download it from below and run it from MATLAB. For a quick demonstration, type "meshdemo2d" or "meshdemond". For more details see the documentation.
To locate the theory of Lie groups within Mathematics, one can say that Lie
groups are groups with some additional structure that permits us to apply
analytic techniques such as differentiation in a group theoretic context.
The working title of this book was Channel Equalization for Everyone. Channel
equalization for everyone? Well, for high school students, channel equalization
provides a simple, interesting example of how Mathematics and physics can be
used to solve real-world problems.
Cooperation has been the subject of intensive study in the social and biological
sciences, as well as in Mathematics and artificial intelligence. The fundamental
finding is that even egoists can sustain cooperation provided the structure of
their environment allows for repeated interactions (Axelrod 1984).
While teaching classes on digital transmission and mobile communications for
undergraduate and graduate students, I was wondering if it would be possible to
write a book capable of giving them some insight about the practical meaning of the
concepts, beyond the Mathematics; the same insight that experience and repetitive
contact with the subject are capable to construct; the insight that is capable of build-
ing the bridge between the theory and how the theory manifests itself in practice.
This book is an entry-level text on the technology of telecommunications. It has been
crafted with the newcomer in mind. The eighteen chapters of text have been prepared
for high-school graduates who understand algebra, logarithms, and basic electrical prin-
ciples such as Ohm’s law. However, many users require support in these areas so Appen-
dices A and B review the essentials of electricity and Mathematics through logarithms.
