نتایج جستجو برای: joint matrix higher rank numerical range

تعداد نتایج: 2350093  

Journal: :CoRR 2012
Bamdev Mishra Gilles Meyer Silvere Bonnabel Rodolphe Sepulchre

Motivated by the problem of learning a linear regression model whose parameter is a large fixed-rank non-symmetric matrix, we consider the optimization of a smooth cost function defined on the set of fixed-rank matrices. We adopt the geometric framework of optimization on Riemannian quotient manifolds. We study the underlying geometries of several well-known fixed-rank matrix factorizations and...

2018
Maboud F. Kaloorazi Rodrigo C. de Lamare

An efficient, accurate and reliable approximation of a matrix by one of lower rank is a fundamental task in numerical linear algebra and signal processing applications. In this paper, we introduce a new matrix decomposition approach termed Subspace-Orbit Randomized singular value decomposition (SORSVD), which makes use of random sampling techniques to give an approximation to a low-rank matrix....

2009
Kim-Chuan Toh Sangwoon Yun

The affine rank minimization problem, which consists of finding a matrix of minimum rank subject to linear equality constraints, has been proposed in many areas of engineering and science. A specific rank minimization problem is the matrix completion problem, in which we wish to recover a (low-rank) data matrix from incomplete samples of its entries. A recent convex relaxation of the rank minim...

2013
N. BEBIANO Panayiotis Psarrakos

The numerical range of a quadratic operator acting on an indefinite inner product space is shown to have a hyperbolical shape. This result is extended to different kinds of indefinite numerical ranges, namely, indefinite higher rank numerical ranges and indefinite Davis-Wielandt shells.

2017
N. Bebiano J. da Providencia N. BEBIANO Panayiotis Psarrakos

The numerical range of a quadratic operator acting on an indefinite inner product space is shown to have a hyperbolical shape. This result is extended to different kinds of indefinite numerical ranges, namely, indefinite higher rank numerical ranges and indefinite Davis-Wielandt shells.

2009
Kim-Chuan Toh Sangwoon Yun

The affine rank minimization problem, which consists of finding a matrix of minimum rank subject to linear equality constraints, has been proposed in many areas of engineering and science. A specific rank minimization problem is the matrix completion problem, in which we wish to recover a (low-rank) data matrix from incomplete samples of its entries. A recent convex relaxation of the rank minim...

Journal: :IEEE Transactions on Geoscience and Remote Sensing 2019

Journal: :IEEE Transactions on Industrial Electronics 2021

Composite is widely used in the aircraft industry and it essential for manufacturers to monitor its health quality. The most commonly found defects of composite are debonds delamination. Different inner with complex irregular shape difficult diagnosed by using conventional thermal imaging methods. In this article, an ensemble joint sparse low-rank matrix decomposition algorithm proposed applyin...

2001
Klas Nordberg Gunnar Farnebäck

This report defines the rank complement of a diagonalizable matrix (i.e. a matrix which can be brought to a diagonal form by means of a change of basis) as the interchange of the range and the null space. Given a diagonalizable matrix A there is in general no unique matrix Ac which has a range equal to the null space of A and a null space equal to the range of A, only matrices of full rank have...

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