The representation of vector data at variable scales has been widely applied in geographic information systems and map-based services. When the scale changes across a wide range, a complex generalization that involves multiple operations is required to transform the data. To present such complex generalization, we proposed a matrix model to combine different generalization operations into an in...

The Rayleigh-Ritz (RR) procedure, including orthogonalization, constitutes a major bottleneck in computing relatively high-dimensional eigenspaces of large sparse matrices. Although operations involved in RR steps can be parallelized to a certain level, their parallel scalability, which is limited by some inherent sequential steps, is lower than dense matrix-matrix multiplications. The primary ...

Recent years witnessed the proliferation of the notion of sparsity and its applications in operations research models. To bring to the attention and raise the interest of the operations research community on this topic, we present in this tutorial a wide range of complex models that admit sparse yet effective solutions. Our examples range from compressed sensing and process flexibility to queui...

A Las Vegas type probabilistic algorithm is presented for nding the Frobenius canonical form of an n n matrix T over any eld K. The algorithm requires O~(MM(n)) = MM(n) (logn) O(1) operations in K, where O(MM(n)) operations in K are suucient to multiply two n n matrices over K. This nearly matches the lower bound of (MM(n)) operations in K for this problem, and improves on the O(n 4) operations...

Consider an invertible n × n matrix over some field. The Gauss-Jordan elimination reduces this matrix to the identity matrix using at most n row operations and in general that many operations might be needed. In [1] the authors considered matrices in GL(n, q), the set of n × n invertible matrices in the finite field of q elements, and provided an algorithm using only row operations which perfor...

A probabilistic algorithm is presented to find the determinant of a nonsingular, integer matrix. For a matrix A n n the algorithm requires O n3 5 logn 4 5 bit operations (assuming for now that entries in A have constant size) using standard matrix and integer arithmetic. Using asymptotically fast matrix arithmetic, a variant is described which requires O n2 2 log2 n loglogn bit operations, wher...

Matrices have been used in many analytical and simulation models and numerical solutions. Matrix operations have essential role in many scientific and engineering applications. One of the most time-consuming operations among matrix operations is matrix inversion. Many hardware designs and software algorithms have been proposed to reduce the time of computation. They will be more important for t...

A probabilistic algorithm is presented to find the determinant of a nonsingular, integer matrix. For a matrix A n n the algorithm requires O n3 5 logn 4 5 bit operations (assuming for now that entries in A have constant size) using standard matrix and integer arithmetic. Using asymptotically fast matrix arithmetic, a variant is described which requires O n2 θ 2 log2 n loglogn bit operations, wh...

To date, parallel simulation algorithms for spiking neural P (SNP) systems are based on a matrix representation. This way, the is implemented with linear algebra operations, which can be easily parallelized high performance computing platforms such as GPUs. Although it has been convenient first generation of GPU-based simulators, CuSNP, there some bottlenecks to sort out. For example, proposed ...