2004 | OriginalPaper | Chapter
Linear systems
Authors : Alfio Quarteroni, Fausto Saleri
Published in: Scientific Computing with MATLAB
Publisher: Springer Berlin Heidelberg
Included in: Professional Book Archive
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
In applied sciences, one is quite often led to face a linear system of the form (5.1)$$Ax = b$$ for the solution of complex problems, where A is a square matrix of dimension n x n whose elements a ij are either real or complex, while x and b are column vectors of dimension n with x representing the unknown solution and b is a given vector. Component-wise, (5.1) can be written as $$\begin{gathered} {a_{11}}{x_1} + {a_{12}}{x_2} + \ldots + {a_{1n}}{x_n} = {b_1}, \hfill \\ {a_{21}}{x_1} + {a_{22}}{x_2} + \ldots + {a_{2n}}{x_n} = {b_2}, \hfill \\ \vdots \vdots \vdots \hfill \\ {a_{n1}}{x_1} + {a_{n2}}{x_2} + \ldots + {a_{nn}}{x_n} = {b_n}, \hfill \\ \end{gathered} $$.