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29
On Recursive Oblique Projectors
"... Abstract—This letter proposes a recursive oblique projector. To understand better the recursive oblique projector, we provide a geometrical interpretation of recursive computation and present a brief numerical example. Index Terms—Adaptive filter, innovation matrix, oblique projection, recursive com ..."
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Abstract—This letter proposes a recursive oblique projector. To understand better the recursive oblique projector, we provide a geometrical interpretation of recursive computation and present a brief numerical example. Index Terms—Adaptive filter, innovation matrix, oblique projection, recursive
Constructive updating/downdating of oblique projectors
, 2006
"... A generalization of the GramSchmidt procedure is achieved by providing equations for updating and downdating oblique projectors. The work is motivated by the problem of adaptive signal representation outside the orthogonal basis setting. The proposed techniques are shown to be relevant to the probl ..."
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Cited by 7 (7 self)
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A generalization of the GramSchmidt procedure is achieved by providing equations for updating and downdating oblique projectors. The work is motivated by the problem of adaptive signal representation outside the orthogonal basis setting. The proposed techniques are shown to be relevant
Characterization of the oblique projector U(VU) † V with application to constrained least squares ✩
, 809
"... We provide a full characterization of the oblique projector U(VU) † V in the general case where the range of U and the null space of V are not complementary subspaces. We discuss the new result in the context of constrained least squares minimization which finds many applications in engineering and ..."
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We provide a full characterization of the oblique projector U(VU) † V in the general case where the range of U and the null space of V are not complementary subspaces. We discuss the new result in the context of constrained least squares minimization which finds many applications in engineering
Characterization of the oblique projector U(VU) † V with application to constrained least squares ✩
, 809
"... We provide a full characterization of the oblique projector U(VU) † V in the general case where the range of U and the null space of V are not complementary subspaces. We discuss the new result in the context of constrained least squares minimization which finds many applications in engineering and ..."
Abstract
 Add to MetaCart
We provide a full characterization of the oblique projector U(VU) † V in the general case where the range of U and the null space of V are not complementary subspaces. We discuss the new result in the context of constrained least squares minimization which finds many applications in engineering
Characterization of the oblique projector U(VU) † V with application to constrained least squares ✩
, 809
"... We provide a full characterization of the oblique projector U(VU) † V in the general case where the range of U and the null space of V are not complementary subspaces. We discuss the new result in the context of constrained least squares minimization which finds many applications in engineering and ..."
Abstract
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We provide a full characterization of the oblique projector U(VU) † V in the general case where the range of U and the null space of V are not complementary subspaces. We discuss the new result in the context of constrained least squares minimization which finds many applications in engineering
CHARACTERIZATION OF THE OBLIQUE PROJECTOR U(V U) † V WITH APPLICATION TO CONSTRAINED LEAST SQUARES
, 809
"... Abstract. We provide a full characterization of the oblique projector U(V U) † V in the general case where the range of U and the null space of V are not complementary subspaces. We discuss the new result in the context of constrained least squares minimization which finds many applications in engi ..."
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Abstract. We provide a full characterization of the oblique projector U(V U) † V in the general case where the range of U and the null space of V are not complementary subspaces. We discuss the new result in the context of constrained least squares minimization which finds many applications
Oblique Matching Pursuit
, 2006
"... A method for selecting a suitable subspace for discriminating signal components through an oblique projection is proposed. The selection criterion is based on the consistency principle introduced by M. Unser and A. Aldroubi and extended by Y. Elder. An effective implementation of this principle for ..."
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Cited by 6 (6 self)
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for the purpose of subspace selection is achieved by updating of the dual vectors yielding the corresponding oblique projector.
The many proofs of an identity on the norm of oblique projections
 Numer. Algorithms
"... Given an oblique projector P on a Hilbert space, i.e., an operator satisfying P 2 = P, which is neither null nor the identity, it holds that ‖P ‖ = ‖I − P ‖. This useful equality, while not widelyknown, has been proven repeatedly in the literature. Many published proofs are reviewed, and simpler o ..."
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Cited by 22 (1 self)
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Given an oblique projector P on a Hilbert space, i.e., an operator satisfying P 2 = P, which is neither null nor the identity, it holds that ‖P ‖ = ‖I − P ‖. This useful equality, while not widelyknown, has been proven repeatedly in the literature. Many published proofs are reviewed, and simpler
The Everywhere Displays Projector: A Device to Create Ubiquitous Graphical Interfaces
, 2001
"... This paper introduces the Everywhere Displays projector, a device that uses a rotating mirror to steer the light from an LCD/DLP projector onto different surfaces of an environment. Issues of brightness, oblique projection distortion, focus, obstruction, and display resolution are examined. Solut ..."
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Cited by 171 (18 self)
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This paper introduces the Everywhere Displays projector, a device that uses a rotating mirror to steer the light from an LCD/DLP projector onto different surfaces of an environment. Issues of brightness, oblique projection distortion, focus, obstruction, and display resolution are examined
ON THE FIELD OF VALUES OF OBLIQUE PROJECTIONS ∗
, 2010
"... Abstract. We highlight some properties of the field of values (or numerical range) W (P) of an oblique projector P on a Hilbert space, i.e., of an operator satisfying P 2 = P. If P is neither null nor the identity, we present a direct proof showing that W (P) = W (I − P), i.e., the field of values ..."
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Cited by 3 (0 self)
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Abstract. We highlight some properties of the field of values (or numerical range) W (P) of an oblique projector P on a Hilbert space, i.e., of an operator satisfying P 2 = P. If P is neither null nor the identity, we present a direct proof showing that W (P) = W (I − P), i.e., the field of values
Results 1  10
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29