Results 1  10
of
4,469
When cache blocking sparse matrix vector multiply works and why
 In Proceedings of the PARA’04 Workshop on the Stateoftheart in Scientific Computing
, 2004
"... Abstract We present new performance models and more compact data structures for cache blocking when applied to sparse matrixvector multiply (SpM×V). We extend our prior models by relaxing the assumption that the vectors fit in cache and find that the new models are accurate enough to predict optimu ..."
Abstract

Cited by 28 (5 self)
 Add to MetaCart
Abstract We present new performance models and more compact data structures for cache blocking when applied to sparse matrixvector multiply (SpM×V). We extend our prior models by relaxing the assumption that the vectors fit in cache and find that the new models are accurate enough to predict
Optimally sparse representation in general (nonorthogonal) dictionaries via ℓ¹ minimization
 PROC. NATL ACAD. SCI. USA 100 2197–202
, 2002
"... Given a ‘dictionary’ D = {dk} of vectors dk, we seek to represent a signal S as a linear combination S = ∑ k γ(k)dk, with scalar coefficients γ(k). In particular, we aim for the sparsest representation possible. In general, this requires a combinatorial optimization process. Previous work considered ..."
Abstract

Cited by 633 (38 self)
 Add to MetaCart
Given a ‘dictionary’ D = {dk} of vectors dk, we seek to represent a signal S as a linear combination S = ∑ k γ(k)dk, with scalar coefficients γ(k). In particular, we aim for the sparsest representation possible. In general, this requires a combinatorial optimization process. Previous work
Decoding by Linear Programming
, 2004
"... This paper considers the classical error correcting problem which is frequently discussed in coding theory. We wish to recover an input vector f ∈ Rn from corrupted measurements y = Af + e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible to rec ..."
Abstract

Cited by 1399 (16 self)
 Add to MetaCart
This paper considers the classical error correcting problem which is frequently discussed in coding theory. We wish to recover an input vector f ∈ Rn from corrupted measurements y = Af + e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible
Stable signal recovery from incomplete and inaccurate measurements,”
 Comm. Pure Appl. Math.,
, 2006
"... Abstract Suppose we wish to recover a vector x 0 ∈ R m (e.g., a digital signal or image) from incomplete and contaminated observations y = Ax 0 + e; A is an n × m matrix with far fewer rows than columns (n m) and e is an error term. Is it possible to recover x 0 accurately based on the data y? To r ..."
Abstract

Cited by 1397 (38 self)
 Add to MetaCart
Abstract Suppose we wish to recover a vector x 0 ∈ R m (e.g., a digital signal or image) from incomplete and contaminated observations y = Ax 0 + e; A is an n × m matrix with far fewer rows than columns (n m) and e is an error term. Is it possible to recover x 0 accurately based on the data y
CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
 California Institute of Technology, Pasadena
, 2008
"... Abstract. Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples. This paper describes a new iterative recovery alg ..."
Abstract

Cited by 770 (13 self)
 Add to MetaCart
algorithm called CoSaMP that delivers the same guarantees as the best optimizationbased approaches. Moreover, this algorithm offers rigorous bounds on computational cost and storage. It is likely to be extremely efficient for practical problems because it requires only matrix–vector multiplies
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
Abstract

Cited by 568 (10 self)
 Add to MetaCart
We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so
The Dantzig selector: statistical estimation when p is much larger than n
, 2005
"... In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y = Ax + z, where x ∈ R p is a parameter vector of interest, A is a data matrix with possibly far fewer rows than columns, n ≪ ..."
Abstract

Cited by 879 (14 self)
 Add to MetaCart
In many important statistical applications, the number of variables or parameters p is much larger than the number of observations n. Suppose then that we have observations y = Ax + z, where x ∈ R p is a parameter vector of interest, A is a data matrix with possibly far fewer rows than columns, n
Sequential minimal optimization: A fast algorithm for training support vector machines
 Advances in Kernel MethodsSupport Vector Learning
, 1999
"... This paper proposes a new algorithm for training support vector machines: Sequential Minimal Optimization, or SMO. Training a support vector machine requires the solution of a very large quadratic programming (QP) optimization problem. SMO breaks this large QP problem into a series of smallest possi ..."
Abstract

Cited by 461 (3 self)
 Add to MetaCart
This paper proposes a new algorithm for training support vector machines: Sequential Minimal Optimization, or SMO. Training a support vector machine requires the solution of a very large quadratic programming (QP) optimization problem. SMO breaks this large QP problem into a series of smallest
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 ..."
Abstract

Cited by 478 (26 self)
 Add to MetaCart
and time consuming process. The work described here can help in automating much of this process. We will concentrate our e orts on the widely used linear algebra kernels called the Basic Linear Algebra Subroutines (BLAS). In particular, the work presented here is for general matrix multiply, DGEMM. However
Benchmarking Sparse MatrixVector Multiply
, 2006
"... Abstract — We present a benchmark for evaluating the performance of Sparse matrixdense vector multiply (abbreviated as SpMV) on scalar uniprocessor machines. Though SpMV is an important kernel in scientific computation, there are currently no adequate benchmarks for measuring its performance across ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
Abstract — We present a benchmark for evaluating the performance of Sparse matrixdense vector multiply (abbreviated as SpMV) on scalar uniprocessor machines. Though SpMV is an important kernel in scientific computation, there are currently no adequate benchmarks for measuring its performance
Results 1  10
of
4,469