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Subspaces that minimize the condition number of a matrix
Matrix the condition number subspace subspace
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2015/8/10
We define the condition number of a nonsingular matrix on a subspace, and consider the problem of finding a subspace of given dimension that minimizes the condition number of a given matrix. We give a...
FAST ALGORITHM FOR EXTRACTING THE DIAGONAL OF THE INVERSE MATRIX WITH APPLICATION TO THE ELECTRONIC STRUCTURE ANALYSIS OF METALLIC SYSTEMS
Diagonal extraction hierarchical Schur complement electronic structure calculation
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2015/7/14
We propose an algorithm for extracting the diagonal of the inverse matrices arising from electronic structure calculation. The proposed algorithm uses a hierarchical decomposition ofthe computational ...
Sweeping Preconditioner for the Helmholtz Equation:Hierarchical Matrix Representation
Sweeping Preconditioner Helmholtz Equation Hierarchical Matrix Representation
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2015/7/14
The paper introduces the sweeping preconditioner, which is highly efficient for iterative solutions of the variable-coefficient Helmholtz equation including veryhigh-frequency problems. The first cent...
Fast construction of hierarchical matrix representation from matrix–vector multiplication
Fast algorithm Hierarchical matrix construction Randomized singular value decomposition Matrix–vector multiplication Elliptic operator Green’s function
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2015/7/14
We develop a hierarchical matrix construction algorithm using matrix–vector multiplications, based on the randomized singular value decomposition of low-rank matrices. The algorithm uses Oelog nT appl...
Compressed Representation of Kohn−Sham Orbitals via Selected Columns of the Density Matrix
Compressed Representation Kohn− Sham Orbitals Selected Columns Density Matrix
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2015/7/14
Given a set of Kohn−Sham orbitals from an insulating system, we present a simple, robust, efficient, and highly parallelizable method to construct a set of optionally orthogonal, localized basis...
What is...a Random Matrix?
Random Matrix
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2015/7/8
What is...a Random Matrix。
Carries, Shuffling, and An Amazing Matrix
Carry move amazing matrix
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2015/7/7
Carries, Shuffling, and An Amazing Matrix。
Foulkes characters, Eulerian idempotents, and an amazing matrix
Foulkes character Carry Eulerian idempotent Symmetric group
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2015/7/7
Foulkes characters, Eulerian idempotents, and an amazing matrix。
SMVGEAR: A sparse-matrix, vectorized Gear code for atmospheric models
air pollution photochemistry stratospheric photochemistry aqueous chemistry ordinary differential equations
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2015/7/6
SMVGEAR: A sparse-matrix, vectorized Gear code for atmospheric models.
Degree bounds for polynomial verification of the matrix cube
matrix cube polynomial verification
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2015/6/19
In this paper we consider the problem of how to computationally test whether a matrix inequality is positive semidefinite on a semialgebraic set. We propose a family of sufficient conditions using the...
Time-Delayed Decentralized H-Infinity Controller Design for Civil Structures: a Homotopy Method Through Linear Matrix Inequalities
Civil Structures Controller Design
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2015/6/19
Traditional structural feedback control systems are centralized systems, whose applications to large scale structures encounter a number of practical difficulties in terms of system reliability, cost,...
Exact Matrix Completion via Convex Optimization
Matrix completion low-rank matrices convex optimization duality in optimization nuclear norm minimization random matrices noncommutative Khintchine inequality decoupling compressed sensing
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2015/6/17
We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. ...
A SINGULAR VALUE THRESHOLDING ALGORITHM FOR MATRIX COMPLETION
Nuclear norm minimization matrix completion singular value thresholding Lagrange dual function Uzawa’s algorithm and linearized Bregman iteration
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2015/6/17
This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxat...
The Power of Convex Relaxation:Near-Optimal Matrix Completion
Matrix completion low-rank matrices semidefinite programming duality in optimization nuclear norm minimization random matrices and techniques from random matrix theory free probability
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2015/6/17
This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applica...
Matrix Completion with Noise
Matrix completion low-rank matrices semidefinite programming duality in optimization nuclear-norm minimization oracle inequalities compressed sensing
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2015/6/17
On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data m...