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Glossary

gemm = general matrix multiply
gesv = general matrix vector solve
LU-decomposition = factorization of a matrix into the product of lower and upper-triangular matrices
- This is used for dense matrices.
pivot = operation of swapping two rows of a matrix in order to move a chosen element (the pivot element) onto the diagonal
dense matrix = matrix where O(N^2) elements are nonzero.
sparse matrix = matrix where most of the elements are zero.
- Typically a compressed "sparse" storage format is used for matrices containing only O(N) nonzero elements.
matrix block / tile = small sub-matrix consisting of a contiguous range of rows and columns
dot product = product of two vectors, summed over all elements
multigrid = hierarchical method of solving a matrix-vector problem based on coarsening to a smaller size and eventual refinement to the original size
conjugate gradient = optimization method employing successive vector directions based on the gradient of an objective function
preconditioner = approximate matrix inverse leaving a matrix-vector problem "closer" to a solution
arithmetic intensity = floating point operations per byte of data transferred to the processor doing the operations
GFLOPS = 1024^3 floating point operations per second

References

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