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20,306
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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space is not σfinite. p. 13: add after I.2.6.16: I.2.6.17. If X is a compact subset of C not containing 0, and k ∈ N, there is in general no bound on the norm of T −1 as T ranges over all operators with ‖T ‖ ≤ k and σ(T) ⊆ X. For example, let Sn ∈ L(l 2) be the truncated shift: Sn(α1, α2,...) = (0
Tensor Decompositions and Applications
 SIAM REVIEW
, 2009
"... This survey provides an overview of higherorder tensor decompositions, their applications, and available software. A tensor is a multidimensional or N way array. Decompositions of higherorder tensors (i.e., N way arrays with N â¥ 3) have applications in psychometrics, chemometrics, signal proce ..."
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Cited by 723 (18 self)
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processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, etc. Two particular tensor decompositions can be considered to be higherorder extensions of the matrix singular value decompo
sition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum
Parallel Numerical Linear Algebra
, 1993
"... We survey general techniques and open problems in numerical linear algebra on parallel architectures. We first discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing efficient algorithms. We illust ..."
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Cited by 773 (23 self)
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We survey general techniques and open problems in numerical linear algebra on parallel architectures. We first discuss basic principles of parallel processing, describing the costs of basic operations on parallel machines, including general principles for constructing efficient algorithms. We
An Extended Set of Fortran Basic Linear Algebra Subprograms
 ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1986
"... This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers. ..."
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Cited by 523 (68 self)
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This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrixvector operations which should provide for efficient and portable implementations of algorithms for high performance computers.
Automatically tuned linear algebra software
 CONFERENCE ON HIGH PERFORMANCE NETWORKING AND COMPUTING
, 1998
"... This paper describes an approach for the automatic generation and optimization of numerical software for processors with deep memory hierarchies and pipelined functional units. The production of such software for machines ranging from desktop workstations to embedded processors can be a tedious and ..."
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Cited by 478 (26 self)
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much ofthe technology and approach developed here can be applied to the other Level 3 BLAS and the general strategy can have an impact on basic linear algebra operations in general and may be extended to other important kernel operations.
A Compositional Approach to Performance Modelling
, 1996
"... Performance modelling is concerned with the capture and analysis of the dynamic behaviour of computer and communication systems. The size and complexity of many modern systems result in large, complex models. A compositional approach decomposes the system into subsystems that are smaller and more ea ..."
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Cited by 757 (102 self)
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easily modelled. In this thesis a novel compositional approach to performance modelling is presented. This approach is based on a suitably enhanced process algebra, PEPA (Performance Evaluation Process Algebra). The compositional nature of the language provides benefits for model solution as well
Concurrent Constraint Programming
, 1993
"... This paper presents a new and very rich class of (concurrent) programming languages, based on the notion of comput.ing with parhal information, and the concommitant notions of consistency and entailment. ’ In this framework, computation emerges from the interaction of concurrently executing agent ..."
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Cited by 502 (16 self)
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be possible. To reflect this view of computation, [Sar89] develops the cc family of languages. We present here one member of the family, CC(.L,+) (pronounced “cc with Ask and Choose”) which provides the basic operations of blocking Ask and atomic Tell and an algebra of behaviors closed under prefixing
A Query Language and Optimization Techniques for Unstructured Data
, 1996
"... A new kind of data model has recently emerged in which the database is not constrained by a conventional schema. Systems like ACeDB, which has become very popular with biologists, and the recent Tsimmis proposal for data integration organize data in treelike structures whose components can be used ..."
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Cited by 407 (35 self)
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be represented as fixeddepth trees, and on such trees UnQL is equivalent to the relational algebra. The novelty of UnQL consists in its programming constructs for arbitrarily deep data and for cyclic structures. While strictly more powerful than query languages with path expressions like XSQL, UnQL can still
Linear Algebra Operators for GPU Implementation of Numerical Algorithms
 ACM Transactions on Graphics
, 2003
"... In this work, the emphasis is on the development of strategies to realize techniques of numerical computing on the graphics chip. In particular, the focus is on the acceleration of techniques for solving sets of algebraic equations as they occur in numerical simulation. We introduce a framework for ..."
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Cited by 324 (9 self)
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for the implementation of linear algebra operators on programmable graphics processors (GPUs), thus providing the building blocks for the design of more complex numerical algorithms. In particular, we propose a stream model for arithmetic operations on vectors and matrices that exploits the intrinsic parallelism
Algebraic methods in the theory of lower bounds for boolean circuit complexity
 IN PROCEEDINGS OF THE 19TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING, STOC ’87
, 1987
"... We use algebraic methods to get lower bounds for complexity of different functions based on constant depth unbounded fanin circuits with the given set of basic operations. In particular, we prove that depth k circuits with gates NOT, OR and MOD, where p is a prime require Ezp(O(n’)) gates to calcu ..."
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Cited by 329 (1 self)
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We use algebraic methods to get lower bounds for complexity of different functions based on constant depth unbounded fanin circuits with the given set of basic operations. In particular, we prove that depth k circuits with gates NOT, OR and MOD, where p is a prime require Ezp(O(n’)) gates
Results 1  10
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20,306