We describe an algorithm that, given any full-rank matrix A having fewer rows than columns, can rapidly compute the orthogonal projection of any vector onto the null space of A, as well as the orthogonal projection onto the row space of A, provided that both A and its adjoint A can be applied rapidly to arbitrary vectors. As an intermediate step, the algorithm solves the overdetermined linear l...

Variable order affine projection algorithms have been recently presented to be used when not only the convergence speed of the algorithm has to be adjusted but also its computational cost and its final residual error. These kind of affine projection (AP) algorithms improve the standard AP algorithm performance at steady state by reducing the residual mean square error. Furthermore these algorit...

We propose a fast algorithm for far-field SAR imaging based on a new fast back-projection algorithm developed for tomography. We also modify the algorithm for the near-field scenario. The fast back-projection algorithm for SAR has computational complexity . Compared to traditional FFT-based methods, our new algorithm has potential advantages: the new algorithm does not need frequency-domain int...

A widely applicable approach to visualizing properties of high-dimensional data is to view the data as a linear projection into twoor three-dimensional space. However, developing an appropriate linear projection is often difficult. Information can be lost during the projection process, and many linear projection methods only apply to a narrow range of qualities the data may exhibit. We propose ...

The PROJECTION algorithm by Buhler and Tompa is one of the best existing methods for solving hard motif discovery problems for monad motifs of fixed length l. In this paper we introduce the AGGREGATION algorithm, which like PROJECTION projects all l-mers from the given input sequences into buckets, but uses a different scheme for selecting buckets for subsequent refinement search. This new neig...

Dykstra’s alternating projection algorithm was proposed to treat the problem of finding the projection of a given point onto the intersection of some closed convex sets. In this paper, we first apply Dykstra’s alternating projection algorithm to compute the optimal approximate symmetric positive semidefinite solution of the matrix equations AXB = E, CXD = F. If we choose the initial iterative m...

Regarding the point projection and inversion problem, a classical algorithm for orthogonal projection onto curves and surfaces has been presented by Hu and Wallner (2005). The objective of this paper is to give a convergence analysis of the projection algorithm. On the point projection problem, we give a formal proof that it is second order convergent and independent of the initial value to pro...

The Peirce quincuncial projection is a mapping of the surface of a sphere to the interior of a square. It is a conformal mapping except for four points on the equator. These points of non-conformality cause significant artifacts in photographic applications. In this paper, we propose an algorithm and userinterface to mitigate these artifacts. Moreover, in order to facilitate an interactive user...

An online algorithm is proposed in this letter to optimize the Projection Matrix and Sparsifying Dictionary (PMSD) simultaneously on a large training dataset. A closedform solution is derived for optimizing the projection matrix with a fixed sparsifying dictionary and the stochastic method is used to optimize the sparsifying dictionary with a fixed optimized projection matrix on a large trainin...

Combining the techniques of the working set identification and generalized gradient projection, we present a new generalized gradient projection algorithm for minimax optimization problems with inequality constraints. In this paper, we propose a new optimal identification function, from which we provide a new working set. At each iteration, the improved search direction is generated by only one...