Automatic Preconditioning by Limited Memory Quasi-Newton Updating
نویسندگان
چکیده
منابع مشابه
Automatic Preconditioning by Limited Memory Quasi-Newton Updating
This paper proposes a preconditioner for the conjugate gradient method (CG) that is designed for solving systems of equations Ax = bi with different right-hand-side vectors or for solving a sequence of slowly varying systems Akx = bk. The preconditioner has the form of a limited memory quasi-Newton matrix and is generated using information from the CG iteration. The automatic preconditioner doe...
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The paper proposes a preconditioner for the conjugate gradient method CG that is designed for solving systems of equations Ax bi with di erent right hand side vec tors or for solving a sequence of slowly varying systems Akx bk The preconditioner has the form of a limited memory quasi Newton matrix and is generated using infor mation from the CG iteration The automatic preconditioner does not re...
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where U = V k−mV k−m+1 · · ·V k−1. For the L-BFGS, we need not explicitly store the approximated inverse Hessian matrix. Instead, we only require matrix-vector multiplications at each iteration, which can be implemented by a twoloop recursion with a time complexity of O(mn) (Jorge & Stephen, 1999). Thus, we only store 2m vectors of length n: sk−1, sk−2, · · · , sk−m and yk−1,yk−2, · · · ,yk−m w...
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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2000
ISSN: 1052-6234,1095-7189
DOI: 10.1137/s1052623497327854