With sparse matrix storage, it is in general practical to store the rows of \ mathbf { J } _ \ mathbf { r } in a compressed form ( " eg ", without zero entries ), making a direct computation of the above product tricky due to the transposition.
42.
The natural implementation of sparse matrix arithmetic on a computer makes it easy to compute the sequence " S " in parallel for a number of vectors equal to the width of a machine word indeed, it will normally take no longer to compute for that many vectors than for one.
43.
In the preceding year, he received the John von Neumann Theory Prize from the Operations Research Society of America ( now Institute for Operations Research and the Management Sciences, INFORMS ) for his contributions in the theory of three fields : portfolio theory; sparse matrix methods; and simulation language programming ( SIMSCRIPT ).
44.
In 1995, nullspace of a large sparse matrix over GF ( 2 ); since the set of people interested in large sparse matrices over finite fields and the set of people interested in large eigenvalue problems scarcely overlap, this is often also called the " block Lanczos algorithm " without causing unreasonable confusion.
45.
The little research that has been done on this feature indicates that it may not be trivial to get high performance gains by using MPI-IO . For example, an implementation of sparse matrix-vector multiplications using the MPI I / O library shows a general behaviour of negligible performance gain, but these results are inconclusive.
46.
*T . Bouwmans, N . Aybat, and E . Zahzah . " 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)
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