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223
Ktheory for operator algebras
 Mathematical Sciences Research Institute Publications
, 1998
"... p. XII line5: since p. 12: I blew this simple formula: should be α = −〈ξ, η〉/〈η, η〉. p. 2 I.1.1.4: The RieszFischer Theorem is often stated this way today, but neither Riesz nor Fischer (who worked independently) phrased it in terms of completeness of the orthogonal system {e int}. If [a, b] is a ..."
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Cited by 558 (0 self)
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Neumann used the same name for Hilbert spaces in the modern sense (complete inner product spaces), which he defined in 1928. p. 3 line6: At the end of the line, 2ɛ should be 4ɛ. p. 3 I.1.2.3: The statement that a dense subspace of a Hilbert space H contains an orthonormal basis for H can be false if H
A subspace approach to balanced truncation for model reduction of nonlinear control systems
 International Journal on Robust and Nonlinear Control
, 2002
"... of nonlinear control systems ..."
Truncation Strategies For Optimal Krylov Subspace Methods
 SIAM J. Numer. Anal
, 1999
"... Optimal Krylov subspace methods like GMRES and GCR have to compute an orthogonal basis for the entire Krylov subspace to compute the minimal residual approximation to the solution. Therefore, when the number of iterations becomes large, the amount of work and the storage requirements become excessiv ..."
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Cited by 47 (7 self)
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. GMRES, GCR, restart, truncation, Krylov subspace methods, iterative methods, nonHermitian linear systems AMS subject classifications. Primary, 65F10; Secondary, 15A18, 65N22 PII. S0036142997315950 1.
Subspace Mappings for Image Sequences
 In: Proc. Workshop Statistical Methods in Video Processing
, 2002
"... We consider the use of lowdimensional linear subspace models to infer one highdimensional signal from another, for example, predicting an image sequence from a related image sequence. In the memoryless case the subspaces are found by rankconstrained division, and inference is an inexpensive seque ..."
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Cited by 10 (0 self)
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sequence of projections. In the finitememory case, the subspaces form a linear dynamical system that is identified via factorization, and inference is Kalman filtering. In both cases we give novel closedform solutions for all parameters, with optimality properties for truncated subspaces. Our
FINDING STRUCTURE WITH RANDOMNESS: PROBABILISTIC ALGORITHMS FOR CONSTRUCTING APPROXIMATE MATRIX DECOMPOSITIONS
"... Lowrank matrix approximations, such as the truncated singular value decomposition and the rankrevealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which demonstrates that randomization offers a powerful tool for ..."
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Cited by 253 (6 self)
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Lowrank matrix approximations, such as the truncated singular value decomposition and the rankrevealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which demonstrates that randomization offers a powerful tool
Subspace Communication
, 2014
"... We are surrounded by electronic devices that take advantage of wireless technologies, from our computer mice, which require little amounts of information, to our cellphones, which demand increasingly higher data rates. Until today, the coexistence of such a variety of services has been guaranteed by ..."
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We are surrounded by electronic devices that take advantage of wireless technologies, from our computer mice, which require little amounts of information, to our cellphones, which demand increasingly higher data rates. Until today, the coexistence of such a variety of services has been guaranteed by a fixed assignment of spectrum resources by regulatory agencies. This has resulted into a blind alley, as current wireless spectrum has become an expensive and a scarce resource. However, recent measurements in dense areas paint a very different picture: there is an actual underutilization of the spectrum by legacy systems. Cognitive radio exhibits a tremendous promise for increasing the spectral efficiency for future wireless systems. Ideally, new secondary users would have a perfect panorama of the spectrum usage, and would opportunistically communicate over the available resources without degrading the primary systems. Yet in practice, monitoring the spectrum resources, detecting available resources for opportunistic communication, and transmitting over the resources are hard tasks. This thesis addresses the tasks of monitoring, de
SESOPTN: Combining sequential subspace optimization with truncated Newton method
 Israel Inst. Technol., Sep. 2008 [Online]. Available: http://www.optimizationonline.org/DB_FILE/2008/09/2098.pdf
"... We present a method for very large scale unconstrained optimization of smooth functions. It combines ideas of Sequential Subspace Optimization (SESOP) [4, 2] with those of the Truncated Newton (TN) method. Replacing TN line search with subspace optimization, we allow Conjugate Gradient (CG) iteratio ..."
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Cited by 1 (0 self)
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We present a method for very large scale unconstrained optimization of smooth functions. It combines ideas of Sequential Subspace Optimization (SESOP) [4, 2] with those of the Truncated Newton (TN) method. Replacing TN line search with subspace optimization, we allow Conjugate Gradient (CG
Subspace Representations of Unstructured Text
"... Since 1970 vectorspace models have been used for information retrieval from unstructured text. The initial simple vectorspace models su#ered the same problems encountered today in searching the internet. These di#culties were significantly relieved by Latent Semantic Indexing (LSI), introduced ..."
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in 1990 and improved through 1995. Starting with the simple vectorspace model's sparse termbydocument matrix, LSI used a truncated singularvalue decomposition to obtain a lowrank approximation, reinforcing similarities between documents. This approach stalled, owing primarily to a lack
Flexible innerouter Krylov subspace methods
 SIAM J. NUMER. ANAL
, 2003
"... Flexible Krylov methodsrefersto a classof methodswhich accept preconditioning that can change from one step to the next. Given a Krylov subspace method, such as CG, GMRES, QMR, etc. for the solution of a linear system Ax = b, instead of having a fixed preconditioner M and the (right) preconditione ..."
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Cited by 34 (2 self)
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general theory is provided encompassing many of these cases, including truncated methods. The overall space where the solution is approximated is no longer a Krylov subspace but a subspace of a larger Krylov space. We show how this subspace keeps growing as the outer iteration progresses, thus providing a
Results 1  10
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