[lang] Implement experimental CG(Conjugate Gradient) solver in Taichi-lang #7690
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…-lang (taichi-dev#7690) Issue: taichi-dev#7634 ### Brief Summary This PR implements a matrix-free CG (Conjugate-Gradient) solver in Taichi. The solver targets to solve the linear equation system: $$ Ax = b$$ where $A$ is implicitly represented as a `LinearOperator` instead of a explicitly stored matrix, hence the name "matrix-free". --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
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…-lang (taichi-dev#7690) Issue: taichi-dev#7634 ### Brief Summary This PR implements a matrix-free CG (Conjugate-Gradient) solver in Taichi. The solver targets to solve the linear equation system: $$ Ax = b$$ where $A$ is implicitly represented as a `LinearOperator` instead of a explicitly stored matrix, hence the name "matrix-free". --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
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### Brief Summary This PR implements a matrix-free BICGSTAB (Biconjugate-Gradient Stabilized) solver in Taichi. The solver targets to solve the linear equation system: $$ Ax = b$$ where $A$ is implicitly represented as a `LinearOperator` instead of a explicitly stored matrix, hence the name "matrix-free". BICGSTAB targets at non-symmetric matrix `A`, while `MatrixFreeCG` targets at symmetric matrix. Related #PR 7690 (#7690) --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
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### Brief Summary This PR implements a matrix-free BICGSTAB (Biconjugate-Gradient Stabilized) solver in Taichi. The solver targets to solve the linear equation system: $$ Ax = b$$ where $A$ is implicitly represented as a `LinearOperator` instead of a explicitly stored matrix, hence the name "matrix-free". BICGSTAB targets at non-symmetric matrix `A`, while `MatrixFreeCG` targets at symmetric matrix. Related #PR 7690 (taichi-dev#7690) --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
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### Brief Summary This PR implements a matrix-free BICGSTAB (Biconjugate-Gradient Stabilized) solver in Taichi. The solver targets to solve the linear equation system: $$ Ax = b$$ where $A$ is implicitly represented as a `LinearOperator` instead of a explicitly stored matrix, hence the name "matrix-free". BICGSTAB targets at non-symmetric matrix `A`, while `MatrixFreeCG` targets at symmetric matrix. Related #PR 7690 (taichi-dev#7690) --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
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Issue: #7634
Brief Summary
This PR implements a matrix-free CG (Conjugate-Gradient) solver in Taichi. The solver targets to solve the linear equation system:
where$A$ is implicitly represented as a
LinearOperatorinstead of a explicitly stored matrix, hence the name "matrix-free".