How this calculation works
Run ten Jacobi sweeps on a two-equation linear system and inspect the residual.
Start from zero and update both coordinates from the previous sweepA worked example
The first sweep yields x=y=1.25. The following sweeps alternate toward 1.
Good to know
Convergence is checked using the iteration matrix’s spectral radius.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Run ten Jacobi sweeps on a two-equation linear system and inspect the residual.
The primary result is labeled “x after ten sweeps”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Convergence is checked using the iteration matrix’s spectral radius.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
The first sweep yields x=y=1.25. The following sweeps alternate toward 1.
Which rule does this calculator apply?
Start from zero and update both coordinates from the previous sweep