Linear Algebra and Matrices Flashcards
(15 cards)
Why is linear algebra important to HPC?
Many scientific and engineering applications use more advanced numerical methods which require solving system of linear equations.
Which method is used for complex meshes?
Finite Volume methods
Which additional consideration does the finite volume method have?
It considers fluxes, the flow of mass, momentum, and energy, between adjacent cells.
How does the finite element method approximate the solution?
It uses expansion functions where are non-zero over a small region of the domain.
What does BLAS stand for?
Basic Linear Algebra Subprograms
What does BLAS do?
BLAS defines a standardised interface for basic vector and matrix operations.
What are the three levels of BLAS routines?
- Level 1: vector-vector
- Level 2: matrix-vector
- Level3 : matrix-matrix
What are the arithmetic intensities of the BLAS levels?
Level 1 and 2 have O(1). Level 3 has O(N)
How does Compressed Sparse Row store a matrix?
The matrix is stored using three one-dimensional arrays.
Why is CSR used?
It can significantly reduce the side of a sparse matrix by not storing any unnecessary elements.
Which three linear algebra benchmarks are used to asses a systems speed?
- Linpack
- High Performance Linpack
- High Performance Conjugate Gradients
How does Linpack assess performance?
It measures Flops with a dense linear algebra workload, asking the system to solve Ax = b using a lower-upper factorisation.
How does HPL assess performance?
It acts the same as Linpack but can change the size of matrices so that floating point performance is close to the peak value.
What does HPL measure?
It measures actual HPL performance which is usually a significant fraction of the theoretical maximum performance.
How does HPCG assess performance?
HPCG is representative of sparse algebra workloads having the system solve a 3D Poisson’s equation using a 27-point stencil.
