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Analysis of a New Krylov subspace enhanced parareal algorithm for time-periodic problems
The classical parareal algorithm for time-periodic problems, solving a periodic-like coarse problem, called the periodic parareal algorithm with...
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Kryging: geostatistical analysis of large-scale datasets using Krylov subspace methods
Analyzing massive spatial datasets using a Gaussian process model poses computational challenges. This is a problem prevailing heavily in...
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Sketching the Krylov subspace: faster computation of the entire ridge regularization path
We propose a fast algorithm for computing the entire ridge regression regularization path in nearly linear time. Our method constructs a basis on...
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General Framework for Deriving Reproducible Krylov Subspace Algorithms: BiCGStab Case
Parallel implementations of Krylov subspace algorithms often help to accelerate the procedure to find the solution of a linear system. However, from...
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Adaptively restarted block Krylov subspace methods with low-synchronization skeletons
With the recent realization of exascale performance by Oak Ridge National Laboratory’s Frontier supercomputer, reducing communication in kernels like...
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Randomized block Krylov subspace algorithms for low-rank quaternion matrix approximations
A randomized quaternion singular value decomposition algorithm based on block Krylov iteration (RQSVD-BKI) is presented to solve the low-rank...
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On an integrated Krylov-ADI solver for large-scale Lyapunov equations
One of the most computationally expensive steps of the low-rank ADI method for large-scale Lyapunov equations is the solution of a shifted linear...
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Towards efficient and accurate approximation: tensor decomposition based on randomized block Krylov iteration
Tensor decomposition methods are inefficient when dealing with low-rank approximation of large-scale data. Randomized tensor decomposition has...
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Linearized Krylov subspace Bregman iteration with nonnegativity constraint
Bregman-type iterative methods have received considerable attention in recent years due to their ease of implementation and the high quality of the...
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A Krylov-Schur-like method for computing the best rank-(r1,r2,r3) approximation of large and sparse tensors
The paper is concerned with methods for computing the best low multilinear rank approximation of large and sparse tensors. Krylov-type methods have...
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Rates of robust superlinear convergence of preconditioned Krylov methods for elliptic FEM problems
This paper considers the iterative solution of finite element discretizations of second-order elliptic boundary value problems. Mesh independent...
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Krylov subspace projection method for Sylvester tensor equation with low rank right-hand side
Motivated by the effectiveness of Krylov projection methods and the CP decomposition of tensors, which is a low rank decomposition, we propose...
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An efficient multiscale topology optimization method for frequency response minimization of cellular composites
It is vital to control the vibration of cellular composites under harmonic excitation in engineering. Due to numerous design variables and expensive...
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Krylov Solvers for Interior Point Methods with Applications in Radiation Therapy and Support Vector Machines
Interior point methods are widely used for different types of mathematical optimization problems. Many implementations of interior point methods in...
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A study of defect-based error estimates for the Krylov approximation of φ-functions
Prior recent work, devoted to the study of polynomial Krylov techniques for the approximation of the action of the matrix exponential e t A v , is...
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An economic implementation of the optimal rotated block-diagonal preconditioning method
The numerical discretization of the optimal control problems constrained with certain kind of time-dependent fractional diffusion equations leads to...
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Global GPBiCGstab(L) method for solving linear matrix equations
Global Krylov subspace methods are effective iterative solvers for large linear matrix equations. Several Lanczos-type product methods (LTPMs) for...
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On the convergence of Krylov methods with low-rank truncations
Low-rank Krylov methods are one of the few options available in the literature to address the numerical solution of large-scale general linear matrix...
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The constant solution method for solving large-scale differential Sylvester matrix equations with time invariant coefficients
This paper is mainly focused on the solution of Sylvester matrix differential equations with time-independent coefficients. We propose a new approach...
