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He is listed as an ISI highly cited researcher in mathematics, is the most cited author in the journal Numerical Linear Algebra with Applications, and is the author of the highly cited book Iterative Methods for Sparse Linear Systems. He is a SIAM fellow (class of 2010) and a fellow of the AAAS (2011).
The GMRES method was developed by Yousef Saad and Martin H. Schultz in 1986. It is a generalization and improvement of the MINRES method due to Paige and Saunders in 1975. The MINRES method requires that the matrix is symmetric, but has the advantage that it only requires handling of three vectors.
Successive over-relaxation. In numerical linear algebra, the method of successive over-relaxation ( SOR) is a variant of the Gauss–Seidel method for solving a linear system of equations, resulting in faster convergence. A similar method can be used for any slowly converging iterative process .
In numerical mathematics, relaxation methods are iterative methods for solving systems of equations, including nonlinear systems. Relaxation methods were developed for solving large sparse linear systems, which arose as finite-difference discretizations of differential equations.
In the field of numerical analysis, a sparse matrix is a matrix populated primarily with zeros as elements of the table. By contrast, if the number of non-zero elements in a matrix is relatively large, then it is commonly considered a dense matrix. The fraction of zero elements (non-zero elements) in a matrix is called the sparsity (density).
In mathematics, series acceleration is one of a collection of sequence transformations for improving the rate of convergence of a series. Techniques for series acceleration are often applied in numerical analysis, where they are used to improve the speed of numerical integration.
Arnoldi iteration. In numerical linear algebra, the Arnoldi iteration is an eigenvalue algorithm and an important example of an iterative method. Arnoldi finds an approximation to the eigenvalues and eigenvectors of general (possibly non- Hermitian) matrices by constructing an orthonormal basis of the Krylov subspace, which makes it ...
George C. Papanicolaou ( / ˌpæpəˈnɪkəlaʊ /; born January 23, 1943) is a Greek - American mathematician who specializes in applied and computational mathematics, partial differential equations, and stochastic processes. [1] He is currently the Robert Grimmett Professor in Mathematics at Stanford University .
The John von Neumann Prize (until 2019 named John von Neumann Lecture Prize [1]) was funded in 1959 with support from IBM and other industry corporations, and began being awarded in 1960 for "outstanding and distinguished contributions to the field of applied mathematical sciences and for the effective communication of these ideas to the ...
Gradient descent is a method for unconstrained mathematical optimization. It is a first-order iterative algorithm for finding a local minimum of a differentiable multivariate function . The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the ...