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Category: itl Component type:concept
Description
An ITL Interface provides the basic linear operations required by iterative solvers.
• Conjugate Gradient(cg)  mult(A, x, y, z); z = y + A * x mult(A, x, y); y = A * x scaled(x, alpha); Delaying scaling vector x size(x); The dimension of vector space solve(M, x, y); Solving preconditioner system dot_conj(x, y); Conjugate inner product: x * yT add(x, y, z); z = x + y copy(x, y); Copying elements of x to resulting vector y two_norm(x); The two norm of x
• Conjugate Gradient Squared (cgs)  mult(A, x, y, z); z = y + A * x mult(A, x, y); y = A * x scaled(x, alpha); Delaying scaling vector x size(x); The dimension of vector space solve(M, x, y); Solving preconditioner system dot(x, y); Inner product: x * y add(x, y); y += x add(x, y, z); z = x + y copy(x, y); Copying elements of x to resulting vector y two_norm(x); The two norm of x
• BiConjugate Gradient (bicg)  mult(A, x, y, z); z = y + A * x mult(A, x, y); y = A * x trans_mult(A, x, y); y = AT * x scaled(x, alpha); Delaying scaling vector x size(x); The dimension of vector space solve(M, x, y); Solving preconditioner system trans_solve(M, x, y); Solving tranpose preconditioner system dot(x, y); Inner product: x * y add(x, y, z); z = x + y copy(x, y); Copying elements of x to resulting vector y two_norm(x); The two norm of x
• BiConjugate Gradient Stabilized (bicgstab)  mult(A, x, y, z); z = y + A * x mult(A, x, y); y = A * x scaled(x, alpha); Delaying scaling vector x size(x); The dimension of vector space solve(M, x, y); Solving preconditioner system dot(x, y); Inner product: x * y add(x, y, z); z = x + y copy(x, y); Copying elements of x to resulting vector y two_norm(x); The two norm of x
• Chebyshev Iteration (cheby)  mult(A, x, y, z); z = y + A * x mult(A, x, y); y = A * x scaled(x, alpha); Delaying scaling vector x size(x); The dimension of vector space solve(M, x, y); Solving preconditioner system add(x, y, z); z = x + y copy(x, y); Copying elements of x to resulting vector y two_norm(x); The two norm of x
• Richardson Iteration (richardson)  mult(A, x, y, z); z = y + A * x scaled(x, alpha); Delaying scaling vector x size(x); The dimension of vector space solve(M, x, y); Solving preconditioner system add(x, y); y += x two_norm(x); The two norm of x
• Generalized Conjugate Residual (gcr)  mult(A, x, y, z); z = y + A * x mult(A, x, y); y = A * x scaled(x, alpha); Delaying scaling vector x size(x); The dimension of vector space solve(M, x, y); Solving preconditioner system dot_conj(x, y); Conjugate inner product: x * yT add(x, y, z); z = x + y copy(x, y); Copying elements of x to resulting vector y two_norm(x); The two norm of x internal_matrix_traits::Matrix Internal matrix type
• Generalized Minimal Residual (gmres)  mult(A, x, y, z); z = y + A * x mult(A, x, y); y = A * x scaled(x, alpha); Delaying scaling vector x scale(x, alpha); Scaling vector x size(x); The dimension of vector space solve(M, x, y); Solving preconditioner system dot_conj(x, y); Conjugate inner product: x * yT add(x, y); y += x copy(x, y); Copying elements of x to resulting vector y two_norm(x); The two norm of x internal_matrix_traits::Matrix Internal matrix type upper_tri_solve(A, x, i); Backward substitution for upper triangular part of Hessenberg matrix Orthogonalizer; To perform orthogonalization
• Quasi-Minimal Residual Without Lookahead (qmr)  mult(A, x, y, z); z = y + A * x mult(A, x, y); y = A * x trans_mult(A, x, y); y = AT * x scaled(x, alpha); Delaying scaling vector x scale(x, alpha); Scaling vector x size(x); The dimension of vector space solve(M, x, y); Solving preconditioner system trans_solve(M, x, y); Solving tranpose preconditioner system dot(x, y); Inner product: x * y add(x, y); y += x add(x, y, z); z = x + y copy(x, y); Copying elements of x to resulting vector y two_norm(x); The two norm of x
• Transpose Free Quasi-Minimal Residual Without Lookahead (tfqmr)  mult(A, x, y, z); z = y + A * x mult(A, x, y); y = A * x scaled(x, alpha); Delaying scaling vector x size(x); The dimension of vector space solve(M, x, y); Solving preconditioner system dot(x, y); Inner product: x * y add(x, y, z); z = x + y add(x, y, z, r); r = x + y + z copy(x, y); Copying elements of x to resulting vector y two_norm(x); The two norm of x
Models
Notes