![]() (1991), "Solving Large Sparse Linear Systems Over Finite Fields", Advances in Cryptology – CRYPT0' 90, Lecture Notes in Computer Science, vol. 537, p. 109, doi: 10.1007/4-3_8, ISBN 978-8-8 (1986), "Solving sparse linear equations over finite fields" (PDF), IEEE Transactions on Information Theory, 32: 54–62, doi: 10.1109/TIT.1986.1057137 "Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method". (2006), Google's PageRank and beyond: the science of search engine rankings, Princeton University Press, p. 40, ISBN 978-2-1 Manipulating and calculating this vector is easier than working with a large matrix or linear system. In order to remove the need to calculate the Jacobian, the Jacobian vector product is formed instead, which is in fact a vector itself. To avoid this expense, matrix-free methods are employed. Solving these equations requires the calculation of the Jacobian which is costly in terms of CPU time and storage. ![]() Matrix-free conjugate gradient method has been applied in the non-linear elasto-plastic finite element solver. It is generally used in solving non-linear equations like Euler's equations in computational fluid dynamics.
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