Krylov算法也是如此,全称是Krylov Subspace Methods 或者 Krylov Subspace Iteration Method。实际指的是,利用Krylov这种思想,用迭代的方式,建立一个合理的子空间,在这个子空间中求解矩阵运算的问题,从而来逼近要求的解。在不同的问题上,比如:线性方程组问题、还是特征值问题、还是广义特征值问题等,Krylov算法的形式都不...
Linearized Bregman iterationIll-posed problemKrylov subspaceNonnegativity constraintBregman-type iterative methods have received considerable attention in recent years due to their ease of implementation and the high quality of the computed solutions they deliver. However, these iterative methods may require ...
resultsshowthatthethreeKrylovsubspaceiterationmethodsareabletoresolvethemulti-dimensionrecursive equationsevenonbigparallelscale. Keywords:parallel;Multi-dimension;RecursiveEquations;KrylovSubspaceMethods;PCG;ATCG;GMRES 摘要:多维递归方程组在并行求解时存在串并行不一致问题,本文提供了三种Krylov子空间迭代求解方法—— PC...
In order to reduce the computational complexity of DOA estimation algorithms and improve their estimation accuracy under large array elements, this paper proposes a DOA estimation method based on Krylov subspace and weighted l1...
[1950: Magnus Hestenes, Eduard Stiefel, and Cornelius Lanczos, all from the Institute for Numerical Analysis at the National Bureau of Standards, initiate the development of Krylov subspace iteration methods.] Krylov子空间方法在提高大型科学和工程计算效率上起着重要作用。
defarnoldi_iteration(A, b, n:int): """Compute a basis of the (n + 1)-Krylov subspace of the matrix A. This is the space spanned by the vectors {b, Ab, ..., A^n b}. Parameters --- A : array_like An m × m array. b : array...
试验表明这三种Krylov子空间 迭代法在并行规模较大的情况下,均能够正确求解多维递归方程组,并且加速特性良好。 关键词 并行 多维 递归方程组 Krylov子空间迭代法 PCGATCGGMRES 中图分类号 TN401 文献标识码 A DOI:10.3969/j.issn.1000386x.2012.11.022 THREEKRYLOVSUBSPACEITERATIONMETHODSFORPARALLELCOMPUTATION OF...
In our method, we construct on each iteration a Krylov subspace formed by the gradient and an approximation to the Hessian matrix, and then use a subset of the training data samples to optimize over this subspace. As with the Hessian Free (HF) method of [7], the Hessian matrix is never...
Krylov subspace methods – p. 15 Augmented method. Spectral Information available. Structural Dynamics problem: (AB −1 +σI)x = b A, B complex sym. n = 86, 000. Solve for σ in a wide interval Note: at each iteration solve system with matrix B B = B(κ) κ related to arti...
解決Krylov 子空間基底蘊含的病態問題的最直接方法是正交化 Krylov 向量序列。給定 階矩陣 與種子向量 , ,假設 是Krylov 子空間 的一組單範正交基底 (orthonormal basis)。如果 ,欲建構 ,使用 Gram-Schmidt 正交化程序:扣除 至基底向量 的投影量 (見“Gram-Schmidt 正交化與 QR 分解”)...