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Linear Algebra
Published in Erchin Serpedin, Thomas Chen, Dinesh Rajan, Mathematical Foundations for SIGNAL PROCESSING, COMMUNICATIONS, AND NETWORKING, 2012
Fatemeh Hamidi Sepehr, Erchin Serpedin
is a linear transformation, and matrix A is referred to as the matrix representation of transformation TA• The rank of matrix A is by definition the dimension of range space of TA• In addition, the column (row) rank of matrix A is defined to be the largest number of independent columns (rows) of A. The following result merges together the concepts of row rank, column rank, and rank of matrix.
An adaptive approach for compression format based on bagging algorithm
Published in International Journal of Parallel, Emergent and Distributed Systems, 2023
Cui Huanyu, Han Qilong, Wang Nianbin, Wang Ye
CSR(Compressed Sparse Row) [13, 14] is a common sparse matrix representation format. The CSR format uses three arrays to store data :VAL, COL, and OFFSET. Where VAL stores the value of the non-zero element, COL stores the column coordinate of the non-zero element, and OFFSET stores the offset of the number of non-zero elements. Assuming that matrix A is a sparse matrix of 6*6, the CSR compressed format is shown in Figure 3: As can be seen from the description of CSR storage, CSR format can store a sparse matrix composed of three arrays, saving storage space and reducing calculation redundancy to a certain extent. However, the data stored in CSR format is discontinuous, which leads to the discontinuity of memory access, thus affecting the computing efficiency during parallel SPMV.
Sparse Compression-Based Image Encryption using Data Encryption Standards RC5
Published in IETE Technical Review, 2023
Arghya Pathak, Hrishikesh Mondal, Jayashree Karmakar, Subhashish Pal, Debasish Nandi, Mrinal Kanti Mandal
In general, images and videos contain large amounts of data and applying data encryption algorithms takes a long time to process and requires large memory space. Moreover, confusion and diffusion techniques used to generate cipher images from the original are prone to different types of attacks. To combat these problems, we have adopted a sparse representation technique to reduce the data size and applied the renowned RC5 algorithm [13] for encryption purposes. This technique not only creates enormous confusion but also diffuses the pixel information efficiently. Over the past few years, the sparse representation of images has attracted researchers due to some of its unique advantages [25]. The sparse approach of an image has been successfully used in different image processing applications like super-resolution, inpainting, denoising, encryption, etc. of greyscale [25–27] and colored images [25, 28–30]. An image in the sparse domain can be represented by the linear combination of a few sparse vectors or atoms containing a few nonzero or significant coefficients [31]. So, after desirable compression without reducing much quality, it is sufficient to encode the non-zero coefficients for further encryption. The pixels of a digital image have a high correlation among them. Therefore, direct encryption of the image pixel may reduce security. Sparse matrix representation of an image has the main advantage that its elements have less correlation among themselves, thus enhancing security.
An improved stiff-ODE solving framework for reacting flow simulations with detailed chemistry in OpenFOAM
Published in Combustion Theory and Modelling, 2023
Kun Wu, Yuting Jiang, Zhijie Huo, Di Cheng, Xuejun Fan
However, as the size of the chemical mechanisms increases, the inherent sparsity of the combustion chemistry suggests that a sparse matrix representation should be preferred. As a result, for large-scale chemical kinetics, sparse matrix representation with associated sparse matrix algebra is implemented in the present framework. Following Imren and Haworth [15], the advanced sparse matrix algebra is realised by the latest version of the KLU library which is a part of the SuiteSparse package [38]. It should be noted that for high fidelity simulation with detailed chemistries as we are concerned, the involved chemical mechanisms may span a wide range in the number of species and reactions. As a matter of fact, the question here is to determine suitable combinations of ODE-integration algorithm, Jacobian evaluation formulation, and linear system solver for a certain level of chemistry complexity, which is one of the main concerns for the present study.