# Solving a Linear System with Uncertain Coefficients

Solving a Linear System with Uncertain Coefficients

This Demonstration shows the LinearSolve solution of linear algebraic systems with uncertain numbers of the form as entries. The rules are extracted from the authors' Uncertain Calculus package. The elements of the initialization diagonal matrix and right-hand side vector are . The "size" of the linear system can be set from 2×2 to 10×10.

x±Δx

1±0.

A slider is used to set the "real" and "uncertain" parts of the matrix and the vector's uncertain entries for selected "row" and "column". The slider intervals for the real and uncertain parts of the uncertain number are and , respectively. These values are multiplied by , where ranges from -5 to 5. The slider jump is , where ranges from 1 to 6.

x

Δx

x±Δx

[-1,1]

[0,1]

n

10

n

-p

10

p

For the sizes up to 5, the entire matrix, the solution, and the right-hand side vector are all shown in the pane. For the sizes from 6 to 10, only the acting element of the matrix or vector is shown, but the setting "nothing" lets you inspect the values of the matrix and vector elements by using consecutively the corresponding "row" and "column" controller settings. When all elements of the matrix and vector have zero uncertainty, the solution coincides with the standard one. The uncertainty of elements changes the uncertainty of the solution.