A condensation-based application of Cramerʼs rule for solving large-scale linear systems

AbstractState-of-the-art software packages for solving large-scale linear systems are predominantly founded on Gaussian elimination techniques (e.g. LU-decomposition). This paper presents an efficient framework for solving large-scale linear systems by means of a novel utilization of Cramerʼs rule. While the latter is often perceived to be impractical when considered for large systems, it is shown that the algorithm proposed retains an O(N3) complexity with pragmatic forward and backward stability properties. Empirical results are provided to substantiate the stated accuracy and computational complexity claims

Toward a Sequential Approach to Pipelined Image Recognition

Abstract—This paper introduces a sequentially motivated approach to processing streams of images from datasets with low memory demands. We utilize fuzzy clustering as an incremental dictionary learning scheme and explain how the corresponding membership functions can be subsequently used in encoding features for image patches. We focus on replicating the codebook learning and classification stages from an established visual learning pipeline that has recently shown efficacy on the CIFAR-10 small image dataset. Experiments show that performance near batch oriented learning is achievable by combining naturally online learning mechanisms driven largely by stochastic gradient descent with strictly patch-wise operations. We further detail how backpropagation can be used with a neural network classifier to modify parameters within the pipeline. Index Terms—sequential learning; image recognition; neural networks I