x = bicg(A, b)
x = bicg(A, b, tol, maxit)
x = bicg(A, b, tol, maxit, M1, M2, x0)
[x, flag, relres, iter, resvec] = bicg(...)
| Parameter | Description |
|---|---|
| A | sparse square coefficient matrix. |
| b | right-hand side vector. |
| tol | relative residual tolerance. Default is 1e-6. |
| maxit | maximum number of iterations. |
| M1, M2 | optional preconditioners: sparse or full square matrices, diagonal vectors, or function handles. Function handles must accept a vector and a transpose flag. |
| x0 | initial guess. |
| Parameter | Description |
|---|---|
| x | computed solution. |
| flag | 0 if convergence was reached, 1 if maxit was reached, 4 on numerical breakdown. |
| relres | relative residual norm. |
| iter | number of iterations performed. |
| resvec | residual norm history. |
bicg solves A*x = b using the BiConjugate gradients method.
The method is intended for sparse nonsymmetric systems. It supports sparse or full matrix preconditioners, diagonal vector preconditioners, and function handles.
When M1 or M2 is a matrix, bicg applies it through an internal linear solve. A vector preconditioner is interpreted as the diagonal of a square preconditioner. A function handle must accept a vector and a transpose flag, then return a vector with the same length.
Sparse single and sparse single complex matrices are supported. If M1, M2, or x0 is complex, the computation uses the matching complex solver path.
A = sparse([4 1 0; 2 3 1; 0 1 2]);
b = [1; 2; 3];
[x, flag, relres, iter, resvec] = bicg(A, b, 1e-12, 20)A = sparse([4 1; 2 3]);
b = [5; 5];
M1 = [2 0; 0 1];
M2 = [2 0.5; 2 3];
[x, flag, relres, iter] = bicg(A, b, 1e-12, 10, M1, M2)A = sparse(single([4 1i; 2 3]));
b = single([1; 2]);
[x, flag] = bicg(A, b, 1e-6, 20)| Version | Description |
|---|---|
| 2.0.0 | initial version |
| 2.0.0 | sparse single, sparse single complex, matrix preconditioners, and function handle preconditioners supported. |