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• Matrix-free_methods abstract "In computational mathematics, a matrix-free method is an algorithm for solving a linear system of equations or an eigenvalue problem that does not store the coefficient matrix explicitly, but accesses the matrix by evaluating matrix-vector products. Such methods can be preferable when the matrix is so big that storing and manipulating it would cost a lot of memory and computer time, even with the use of methods for sparse matrices. Many iterative methods allow for a matrix-free implementation, including: the power method, the Lanczos algorithm, Locally Optimal Block Preconditioned Conjugate Gradient Method (LOBPCG), Wiedemann's coordinate recurrence algorithm, and the conjugate gradient method.Distributed solutions have also been explored using coarse-grain parallel software systems to achieve homogeneous solutions of linear systems.It is generally used in solving non-linear equations like Euler's equations in Computational Fluid Dynamics. Solving these equations requires the calculation of the jacobian which is costly in terms of CPU time and storage. To avoid this expense, matrix free methods are employed. In order to remove the need to calculate the jacobian, the jacobian vector product is formed instead, which is in fact a vector itself. Manipulating and calculating this vector is easier than working with a large matrix or linear system.".
• Matrix-free_methods wikiPageID "8515187".
• Matrix-free_methods wikiPageLength "3119".
• Matrix-free_methods wikiPageOutDegree "13".
• Matrix-free_methods wikiPageRevisionID "615305287".
• Matrix-free_methods wikiPageWikiLink Category:Numerical_linear_algebra.
• Matrix-free_methods wikiPageWikiLink Computational_fluid_dynamics.
• Matrix-free_methods wikiPageWikiLink Computational_mathematics.
• Matrix-free_methods wikiPageWikiLink Conjugate_gradient_method.
• Matrix-free_methods wikiPageWikiLink Eigenvalues_and_eigenvectors.
• Matrix-free_methods wikiPageWikiLink Iterative_method.
• Matrix-free_methods wikiPageWikiLink Jacobian_matrix_and_determinant.
• Matrix-free_methods wikiPageWikiLink LOBPCG.
• Matrix-free_methods wikiPageWikiLink Lanczos_algorithm.
• Matrix-free_methods wikiPageWikiLink Matrix_(mathematics).
• Matrix-free_methods wikiPageWikiLink Power_iteration.
• Matrix-free_methods wikiPageWikiLink Sparse_matrix.
• Matrix-free_methods wikiPageWikiLink System_of_linear_equations.
• Matrix-free_methods wikiPageWikiLinkText "Matrix-free methods".
• Matrix-free_methods wikiPageWikiLinkText "matrix-free fashion".
• Matrix-free_methods wikiPageWikiLinkText "matrix-free method".
• Matrix-free_methods wikiPageWikiLinkText "matrix-free methods".
• Matrix-free_methods wikiPageUsesTemplate Template:Mathapplied-stub.
• Matrix-free_methods wikiPageUsesTemplate Template:Numerical_linear_algebra.
• Matrix-free_methods wikiPageUsesTemplate Template:Reflist.
• Matrix-free_methods subject Category:Numerical_linear_algebra.
• Matrix-free_methods hypernym Algorithm.
• Matrix-free_methods type Software.
• Matrix-free_methods comment "In computational mathematics, a matrix-free method is an algorithm for solving a linear system of equations or an eigenvalue problem that does not store the coefficient matrix explicitly, but accesses the matrix by evaluating matrix-vector products. Such methods can be preferable when the matrix is so big that storing and manipulating it would cost a lot of memory and computer time, even with the use of methods for sparse matrices.".
• Matrix-free_methods label "Matrix-free methods".
• Matrix-free_methods sameAs Q4080929.
• Matrix-free_methods sameAs m.027660s.
• Matrix-free_methods sameAs Безматричные_методы.
• Matrix-free_methods sameAs Q4080929.
• Matrix-free_methods wasDerivedFrom Matrix-free_methods?oldid=615305287.
• Matrix-free_methods isPrimaryTopicOf Matrix-free_methods.