A Parallel Adaptive Gauss-Jordan Algorithm

This paper presents a parallel adaptive version of the block-based Gauss-Jordan algorithm, utilized to invert large matrices. This version includes a characterization of the workload and a mechanism of its folding/unfolding. Furthermore, this paper proposes a work scheduling strategy and an application-oriented solution for the fault tolerance problem. The application is implemented and experimented with MARS¹ in dedicated and non-dedicated environments. The results show that an absolute efficiency of 92% is possible on a cluster of DEC/ALPHA processors interconnected by a Gigaswitch network and an absolute efficiency of 67% can be obtained on an Ethernet network of SUN-Sparc 4 workstations. Moreover, the algorithm is tested on a meta-system including both the two parks of machines. Finally, an out-of-core solution for the algorithm is proposed. This solution allows a gain of 66% of data input operations and reduces the central memory space required for storing the data space of the algorithm by a factor q, where q is the dimension of the matrix to be inverted in terms of data blocks.     

Selective color imaging using weighted interleaved multiple annular linear diffractive axicons

Annular linear diffractive axicons are optical devices providing chromatic imaging over an extended depth of focus when illuminated by a white light. To improve their low radiometric performance, multiple annular linear diffractive axicons (MALDAs) have been introduced. Their chromatic properties are well known and constrained by dispersion laws. A first attempt to freely combine colors or wavelength bands has been obtained with interleaved MALDAs (I_MALDAs). However, such optics do not provide a full decoupling between wavelength combination and brightness control required in the CIE color space to address any colors. We present here a new category of I_MALDA providing this capability when illuminated by a white source containing tristimulus (red/green/blue) values. We assess both theoretically and experimentally imaging qualities of such optics with respect to two different interleaving techniques and suggest some potential applications, in particular in the field of anticounterfeit and authentication techniques.