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Optical tomography is a biomedical imaging modality that uses scattered light as a probe of structural variations in the optical properties of tissue [1]. In a typical experiment, a highly-scattering medium is illuminated by a narrow collimated beam and the light that propagates through the medium is collected by an array of detectors. In first generation systems, the sources and detectors are ...

In this paper, diierent strategies to exploit the sparse structure in the solution techniques for macroeconometric models with forward-looking variables are discussed. First, the stacked model is decomposed into recursive submodels without destroying its original block pattern. Next, we concentrate on how to eeciently solve the sparse linear system in the Newton algorithm. In this frame, a mult...

Direct search methods are mainly designed for use in problems with no equality constraints. However, there are many instances where the feasible set is of measure zero in the ambient space and no mesh point lies within it. There are methods for working with feasible sets that are (Riemannian) manifolds, but not all manifolds are created equal. In particular, reductive homogeneous spaces seem to...

Direct volume rendering immediately display the datasets into image plane without any intermediate representation. Commonly this method can be classified into image-order techniques represent a backward-mapping scheme and objectorder techniques apply a forward-mapping scheme. By using the image-order methods image is generated pixel-by-pixel casting rays from the view-point through each pixel o...

Constrained optimization techniques are studied in this paper for direct design of linear multichannel equalizers. Novel blind algorithms are derived by minimizing the equalizer’s output variance subject to appropriate constraints. The constraints are chosen to guarantee no desired signal cancellation, and their parameters are jointly optimized to maximize the signal component at the output. Th...

The preceding design methods have been based on designing an analog prototype lter and then converting it to a digital lter. This approach is appropriate for the class of approximations where analytical solutions are possible, but not for many others. In the remaining part of this chapter, methods will be developed that directly design the desired digital lter. Most approaches are extensions of...

We extend direct search methods to optimization problems that include equality constraints given by Lipschitz functions. The equality constraints are assumed to implicitly define a Lipschitz manifold. Numerically implementing the inverse (implicit) function theorem allows us to define a new problem on the tangent spaces of the manifold. We can then use a direct search method on the tangent spac...

Elliptic problems with oscillating coefficients can be approximated up to arbitrary accuracy by using sufficiently fine meshes, i.e., by resolving the fine scale. Well-known multiscale finite elements [5, 9] can be regarded as direct numerical homogenization methods in the sense that they provide approximations of the corresponding (unfeasibly) large linear systems by much smaller systems while...