Best practices for solving overdetermined systems of linear equations

Newbie
1

ROOT Version: 6.36.04
Platform: ubuntu linux
Compiler: g++

Dear ROOT users,

I would like to know what would be the best practice for solving the following overdetermined system of linear equations (shown as ASCII drawing below):

/                      \   /         \   /       \
| Ar_01  He_01  CO2_01 |   |         |   | IC_01 |
| Ar_02  He_02  CO2_02 |   | Ar__PPM |   | IC_02 |
| Ar_03  He_03  CO2_03 | X | He__PPM | = | IC_03 |
| Ar_04  He_04  CO2_04 |   | CO2_PPM |   | IC_04 |
|...                   |   |         |   | ...   |
| Ar_50  He_50  CO2_50 |   |         |   | IC_50 |
\                      /   \         /   \       /

Where matrix at the left side of the equation and vector at the right side of the equation are known; and least-square solution of vector containing “PPM” entries is required.

Would greatly appreciate any help,

Kind regards,

Daniil Korshkov, Carleton University physics department

P.S. Sorry for ASCII drawing being distorted

2

Hi Daniil,

welcome to the ROOT forum.
Since your question is about linear algebra rather than ROOT, I’d recommend to discuss this with your supervisor. As a starter you could take a look at [1] or a linear algebra textbook.
If you do have a ROOT specific question or problem, please let us know.

Lukas

[1] Overdetermined system - Wikipedia

3

Hello Lukas,

Thank you for reaching out.

Since ROOT is a language specifically designed for solving mathematical problems, and due to workplace requirements I need to solve this problem using ROOT (sorry as I forgot to mention it before), I assumed there are plenty of people on this forum who have expertise solving such problems

Kind regards,

Daniil

4

Let me ping @Eddy_Offermann