Numerical Linear Algebra

By L. Čížková, Pavel Cízek. 2011

2,575 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

Citations in the corpus

Fast distributed coordinate descent for non-strongly convex losses (2014, background): “Note that the ESO assumption will still hold when σ and σ (cid:48) in (13) are replaced by some upper bounds.”
A Survey of Quantization Methods for Efficient Neural Network Inference (2021, neutral): “We refer the interested reader to [229] for a detailed discussion of these issues.”
MINRES-QLP: A Krylov Subspace Method for Indefinite or Singular Symmetric Systems (2010, background): “(cid:2) Then P A ≡ U 1 U T 1 and P ⊥ A ≡ U 2 U T 2 are orthogonal projectors [53] onto the range and nullspace of A .”
P4P: Practical Large-Scale Privacy-Preserving Distributed Computation Robust against Malicious Users (2010, background): “In particular, the error is O ( A 2 /σ k ) [48]. k k Fortunately, most applications (e.g., PCA) only need the k largest singular values (and their singular vectors).”
On selecting a maximum volume sub-matrix of a matrix and related problems (2009, neutral): “But, as is pointed out by Kahan [16], there are matrices where it fails to satisfy the”
The black-box fast multipole method (2009, background): “The solution to this constrained minimization aof (8) is given by a theorem from numerical linear algebra which states that the best rank-r approximation of an n-by-n matrix A, where r 6 n, with respect to the Frobenius norm corresponds to picking the r left and right singular vectors of the SVD of ”
Optimal and reduced quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis (2017, methodology): “The reduced singular value decomposition [23, 49] is used to solve the linearized system of equations if they are singular.”
Fast Random Walk Graph Kernel (2012, background): “The r-approximation gives a good approximation of the original matrix since the singular value decomposition (SVD) gives the best low rank approximation [41].”
The geometric mean decomposition (2005, methodology): “For comparison, reduction of H to bidiagonal form by the Golub–Kahan bidiagonalization scheme [4] (also see [5,6,14,16]), often the first step in the computation of the SVD, requires O(mnK) flops.”
Topology optimization for worst load conditions based on the eigenvalue analysis of an aggregated linear system (2011, background): “Chapter 4 in [41] or Chapter 2 in [42]) as follows:”
Approximate policy iteration: a survey and some new methods (2011, background): “, λs} and U is a unitary matrix (UU ′ = I; see [58,59]).”
Nearly-Linear Time Algorithms for Preconditioning and Solving Symmetric, Diagonally Dominant Linear Systems (2006, background): “These preconditioners improve upon the subgraph preconditioners first introduced by Vaidya (1990). For any M0-matrix A and k ≥ 1, we construct in time m log n a preconditioner of A with at most 2(n− 1 + k) non-zero off-diagonal entries such that the preconditioned system has condition number at most”
Bundle Adjustment in the Large (2010, methodology): “The method of choice for solving symmetric positive definite systems exactly is via the Cholesky factorization [16] and depending upon the structure of the matrix, there are, in general, two options.”
An anisotropic shear velocity model of the Earth's mantle using normal modes, body waves, surface waves and long-period waveforms (2014, methodology): “(13) using a standard Cholesky factorization for positive-definite matrices (e.g. Trefethen & Bau 1997).”
On dynamic mode decomposition: Theory and applications (2013, background): “Compute the (reduced) SVD of X (see [32]), writing”