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Sparse Matrix–vector Multiplication
Sparse matrix–vector multiplication (SpMV) of the form is a widely used computational kernel existing in many scientific applications. The input matrix is sparse. The input vector and the output vector are dense. In the case of a repeated operation involving the same input matrix but possibly changing numerical values of its elements, can be preprocessed to reduce both the parallel and sequential run time of the SpMV kernel. See also * Matrix–vector multiplication In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix (mathematics), matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the n ... * General-purpose computing on graphics processing units#Kernels References Sparse matrices {{DEFAULTSORT:Sparse matrix-vector multiplication ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compute Kernel
In computing, a compute kernel is a routine compiled for high throughput accelerators (such as graphics processing units (GPUs), digital signal processors (DSPs) or field-programmable gate arrays (FPGAs)), separate from but used by a main program (typically running on a central processing unit). They are sometimes called compute shaders, sharing execution units with vertex shaders and pixel shaders on GPUs, but are not limited to execution on one class of device, or graphics APIs. Description Compute kernels roughly correspond to inner loops when implementing algorithms in traditional languages (except there is no implied sequential operation), or to code passed to internal iterators. They may be specified by a separate programming language such as "OpenCL C" (managed by the OpenCL API), as "compute shaders" written in a shading language (managed by a graphics API such as OpenGL), or embedded directly in application code written in a high level language, as in the case of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sparse Matrix
In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of rows or columns. By contrast, if most of the elements are non-zero, the matrix is considered dense. The number of zero-valued elements divided by the total number of elements (e.g., ''m'' × ''n'' for an ''m'' × ''n'' matrix) is sometimes referred to as the sparsity of the matrix. Conceptually, sparsity corresponds to systems with few pairwise interactions. For example, consider a line of balls connected by springs from one to the next: this is a sparse system as only adjacent balls are coupled. By contrast, if the same line of balls were to have springs connecting each ball to all other balls, the system would correspond to a dense matrix. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix–vector Multiplication
In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices and is denoted as . Matrix multiplication was first described by the French mathematician Jacques Philippe Marie Binet in 1812, to represent the composition of linear maps that are represented by matrices. Matrix multiplication is thus a basic tool of linear algebra, and as such has numerous applications in many areas of mathematics, as well as in applied mathematics, statistics, physics, economics, and engineering. Computing matrix products is a central operation in all computational applications of linear algebra. Notation This article will use the following notati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General-purpose Computing On Graphics Processing Units
General-purpose computing on graphics processing units (GPGPU, or less often GPGP) is the use of a graphics processing unit (GPU), which typically handles computation only for computer graphics, to perform computation in applications traditionally handled by the central processing unit (CPU). The use of multiple video cards in one computer, or large numbers of graphics chips, further parallelizes the already parallel nature of graphics processing. Essentially, a GPGPU pipeline is a kind of parallel processing between one or more GPUs and CPUs that analyzes data as if it were in image or other graphic form. While GPUs operate at lower frequencies, they typically have many times the number of cores. Thus, GPUs can process far more pictures and graphical data per second than a traditional CPU. Migrating data into graphical form and then using the GPU to scan and analyze it can create a large speedup. GPGPU pipelines were developed at the beginning of the 21st century for graphi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
