Arnoldi iteration is a typical large sparse matrix algorithm : It does not access the elements of the matrix directly, but rather makes the matrix map vectors and makes its conclusions from their images.
32.
One area is sparse matrix / band matrix handling, and general algorithms from this area, such as Cuthill McKee algorithm, may be applied to find approximate solutions for the graph bandwidth problem.
33.
Fermat has extensive built-in primitives for array and matrix manipulations, such as submatrix, sparse matrix, determinant, normalize, column reduce, row echelon, Smith normal form, and matrix inverse.
34.
With one byte to specify the efficacy of a synapse, and 5 bytes to specify the index of a neuron, an efficient sparse matrix representation of the matrix would require about 6 bytes per synapse.
35.
The implicit solvers must be used, requiring solution of a large sparse matrix system ( via e . g . the conjugate gradient method ), which itself may also be difficult to achieve at interactive frame rates.
36.
Unlike SPICE, which used Modified nodal analysis ( MNA ) to form the system of circuit equations, ASTAP instead used " sparse tableau formulation " ( STA ) to construct and solve a sparse matrix.
37.
There is the alternative option of indirect energy conversion by employing the Indirect Matrix Converter ( Fig . 5 ) or the Sparse matrix converter which was invented by Prof . Johann W . Kolar from the ETH Zurich.
38.
"' Advanced process monitor ( APMonitor ) "', is a modeling language for MINOS, and SNOPT . The APMonitor API provides exact first and second derivatives of continuous functions to the solvers through automatic differentiation and in sparse matrix form.
39.
Handbook on Robust Low-Rank and Sparse Matrix Decomposition : Applications in Image and Video Processing, CRC Press, Taylor and Francis Group, May 2016 . ( more information : http : / / www . crcpress . com / product / isbn / 9781498724623)
40.
In large linear-programming problems "'A "'is typically a sparse matrix and, when the resulting sparsity of "'B "'is exploited when maintaining its invertible representation, the revised simplex algorithm is a much more efficient than the standard simplex method.
