Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; plgContentJComments has a deprecated constructor in /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php on line 25 Call Stack: 0.0001 362592 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0830 1212056 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0830 1212056 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1564 4105368 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1579 4133160 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1587 4150872 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1588 4167880 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1596 4175616 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1596 4175616 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.2081 4411400 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.2097 4428800 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.2103 4449728 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.2202 4518400 13. Joomla\CMS\Plugin\PluginHelper::importPlugin() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:189 0.2202 4518656 14. Joomla\CMS\Plugin\PluginHelper::import() /var/www/astarmathsandphysics/libraries/src/Plugin/PluginHelper.php:182

Solving Simultaneous Equations Using LU Decomposition

Given a system of linear equations in the formwe can use the LU factorisation ofto solve the linear systemin a two-step triangular process.

Letso thatThe solution is obtained by solving recursively the two systems

and


Example: Use LU decomposition to solve

x-2y+3z=4

2x-5y+12z=6

2y-10z=3

we can write the matrix form of the system

The matrix decomposes:

We solve

|From which

Now solve

We have

The original system of equations is