Sparse methods are primarily valuable for systems in which the number of non-zero entries is substantially less than the overall size of the matrix. Such situations are common in physical systems, ...

Presenting an algorithm that solves linear systems with sparse coefficient matrices asymptotically faster than matrix multiplication for any ω > 2. Our algorithm can be viewed as an efficient, ...

Multiplies ( A^{-1} ) with ( B ) to obtain the solution vector ( X ). Provides error handling for cases where the matrix ( A ) is not invertible or input is invalid.

Most linear algebra courses start by considering how to solve a system of linear equations. \[ \begin{align} a_{0,0}x_0 + a_{0,1}x_0 + \cdots a_{0,n-1}x_0 & = b_0 ...

I Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424, Hafez Avenue, Tehran 15914, Iran. E-mails: mdehghan@aut.ac.ir / ...

Grade school math students are likely familiar with teachers admonishing them not to just guess the answer to a problem. But a new proof establishes that, in fact, the right kind of guessing is ...

1 Department of Environmental Health Science, University of Eswatini, Mbabane, Eswatini. 2 Department of Chemistry, University of Eswatini, Kwaluseni, Eswatini. Systems of linear equations or ...