6.56.7  Solving a linear system using the Jacobi iteration method: jacobi_linsolve

The jacobi_linsolve command finds the solution of a linear system of equations using the Jacobi iteration method.

• jacobi_linsolve command takes two mandatory arguments and two optional arguments:
  • A, the matrix of coefficients of a system.
  • b, the right hand side of the system as a list.
  • Optionally, m, an integer indicating the maximum number of iterations (by default m=maxiter, see Section 3.5.7, item 6).
  • Optionally, є, a positive number indicating the error tolerance (by default є=epsilon, see Section 3.5.7, item 9).
  jacobi_linsolve(A,b ⟨ m,є⟩) returns the solution of the system.

Examples.

• Input:

  A:=[[100,2],[2,100]];

  jacobi_linsolve(A,[0,1],1e-12);

  Output:

  ⎡ ⎣

  −0.000200080032,0.0100040016006

  ⎤ ⎦

• Input:
  evalf(linsolve(A,[0,1]))
  Output:

  ⎡ ⎣

  −0.000200080032013,0.0100040016006

  ⎤ ⎦