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, ...

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, ...

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 / ...

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 ...

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.

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 ...