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Computing interior eigenpairs in augmented Krylov subspace produced by Jacobi–Davidson correction equation
As we know, the Jacobi–Davidson iteration method is very efficient for computing both extreme and interior eigenvalues of standard eigenvalue...
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Deflated and restarted Krylov subspace methods for Sylvester tensor equations
Tensor Krylov subspace methods are popular technologies for solving Sylvester tensor equations, among which the GMRES method based on tensor format...
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Large-scale harmonic balance simulations with Krylov subspace and preconditioner recycling
The multi-harmonic balance method combined with numerical continuation provides an efficient framework to compute a family of time-periodic...
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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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Krylov Subspace Methods for Linear Systems Principles of Algorithms
This book focuses on Krylov subspace methods for solving linear systems, which are known as one of the top 10 algorithms in the twentieth century,...
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On shift selection for Krylov subspace based model order reduction
Mechanical systems are often modeled with the multibody system method or the finite element method and numerically described with systems of...
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A flexible short recurrence Krylov subspace method for matrices arising in the time integration of port-Hamiltonian systems and ODEs/DAEs with a dissipative Hamiltonian
For several classes of mathematical models that yield linear systems, the splitting of the matrix into its Hermitian and skew Hermitian parts is...
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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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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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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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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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Classification and Theory of Krylov Subspace Methods
Krylov subspace methods are roughly classified into three groups: ones for Hermitian linear systems, for complex symmetric linear systems, and for...
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DOA estimation of LFM signal based on Krylov subspace method
Direction of arrival estimation of LFM signal is an essential task in radar, sonar, acoustics and biomedical. In this paper, a short time Fourier...
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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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A Low-Rank Global Krylov Squared Smith Method for Solving Large-Scale Stein Matrix Equation
This paper deals with the numerical solution of the large-scale Stein and discrete-time Lyapunov matrix equations. Based on the global Arnoldi...
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The new Krylov subspace methods for solving tensor equations via T-product
In this paper, we present two new subspace methods for solving some linear tensor equations. Using the well-known tensor T -product, we define two new...
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Krylov Subspace Method Using Quantum Computing
The Krylov subspace algorithm uses iterative methods to solve bulky linear equations. It has a time complexity of O(n2) when run on a classical...
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An Efficient Implementation of the Gauss–Newton Method Via Generalized Krylov Subspaces
The solution of nonlinear inverse problems is a challenging task in numerical analysis. In most cases, this kind of problems is solved by iterative...
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Krylov-Subspace Methods for Quadratic Hypersurfaces: A Grossone–based Perspective
We study the role of the recently introduced infinite number grossone, to deal with two renowned Krylov-subspace methods for symmetric (possibly...