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Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
It was originally known as "HECKE and Manin". After a short while it was renamed SAGE, which stands for ‘’Software of Algebra and Geometry Experimentation’’. Sage 0.1 was released in 2005 and almost a year later Sage 1.0 was released. It already consisted of Pari, GAP, Singular and Maxima with an interface that rivals that of Mathematica.
It is generally used in solving non-linear equations like Euler's equations in computational fluid dynamics. Matrix-free conjugate gradient method has been applied in the non-linear elasto-plastic finite element solver. [7] Solving these equations requires the calculation of the Jacobian which is costly in terms of CPU time and storage. To ...
Matrices can be used to compactly write and work with multiple linear equations, that is, systems of linear equations. For example, if A is an m×n matrix, x designates a column vector (that is, n×1-matrix) of n variables x 1, x 2, ..., x n, and b is an m×1-column vector, then the matrix equation =
Microsoft Math contains features that are designed to assist in solving mathematics, science, and tech-related problems, as well as to educate the user. The application features such tools as a graphing calculator and a unit converter. It also includes a triangle solver and an equation solver that provides step-by-step solutions to each problem.
The standard convergence condition (for any iterative method) is when the spectral radius of the iteration matrix is less than 1: ρ ( D − 1 ( L + U ) ) < 1. {\displaystyle \rho (D^{-1}(L+U))<1.} A sufficient (but not necessary) condition for the method to converge is that the matrix A is strictly or irreducibly diagonally dominant .
In matrix inversion however, instead of vector b, we have matrix B, where B is an n-by-p matrix, so that we are trying to find a matrix X (also a n-by-p matrix): = =. We can use the same algorithm presented earlier to solve for each column of matrix X. Now suppose that B is the identity matrix of size n.
Being released in 1983, Xpress was the first commercial LP and MIP solver running on PCs. [4] In 1992, an Xpress version for parallel computing was published, which was extended to distributed computing five years later. [5] Xpress was the first MIP solver to cross the billion matrix non-zero threshold by introducing 64-bit indexing in 2010. [6]