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406,192
Algebraic Methods for Interactive Proof Systems
, 1990
"... We present a new algebraic technique for the construction of interactive proof systems. We use our technique to prove that every language in the polynomialtime hierarchy has an interactive proof system. This technique played a pivotal role in the recent proofs that IP=PSPACE (Shamir) and that MIP ..."
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Cited by 337 (28 self)
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We present a new algebraic technique for the construction of interactive proof systems. We use our technique to prove that every language in the polynomialtime hierarchy has an interactive proof system. This technique played a pivotal role in the recent proofs that IP=PSPACE (Shamir
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 326 (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
Using Linear Algebra for Intelligent Information Retrieval
 SIAM REVIEW
, 1995
"... Currently, most approaches to retrieving textual materials from scientific databases depend on a lexical match between words in users' requests and those in or assigned to documents in a database. Because of the tremendous diversity in the words people use to describe the same document, lexical ..."
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Cited by 671 (18 self)
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, lexical methods are necessarily incomplete and imprecise. Using the singular value decomposition (SVD), one can take advantage of the implicit higherorder structure in the association of terms with documents by determining the SVD of large sparse term by document matrices. Terms and documents represented
Algebraic Methods
 In Integer Programming
, 2001
"... An approach for particle sinking velocity measurements in the 3–400 lm size range and considerations on the effect of temperature on sinking rates ..."
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Cited by 14 (0 self)
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An approach for particle sinking velocity measurements in the 3–400 lm size range and considerations on the effect of temperature on sinking rates
The Algebraic Method
, 2001
"... Combining the effect of an intermediate renormalization prescription (zero momentum subtraction) and the background field method (BFM), we show that the algebraic renormalization procedure needed for the computation of radiative corrections within noninvariant regularization schemes is drastically s ..."
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Cited by 1 (0 self)
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Combining the effect of an intermediate renormalization prescription (zero momentum subtraction) and the background field method (BFM), we show that the algebraic renormalization procedure needed for the computation of radiative corrections within noninvariant regularization schemes is drastically
An algebraic method for publickey cryptography
 MATHEMATICAL RESEARCH LETTERS
, 1999
"... Algebraic key establishment protocols based on the difficulty of solving equations over algebraic structures are described as a theoretical basis for constructing publickey cryptosystems. ..."
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Cited by 148 (1 self)
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Algebraic key establishment protocols based on the difficulty of solving equations over algebraic structures are described as a theoretical basis for constructing publickey cryptosystems.
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
 ACM Trans. Math. Software
, 1982
"... An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerica ..."
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Cited by 645 (21 self)
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An iterative method is given for solving Ax ~ffi b and minU Ax b 112, where the matrix A is large and sparse. The method is based on the bidiagonalization procedure of Golub and Kahan. It is analytically equivalent to the standard method of conjugate gradients, but possesses more favorable
The geometry of algorithms with orthogonality constraints
 SIAM J. MATRIX ANAL. APPL
, 1998
"... In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal proces ..."
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Cited by 631 (1 self)
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processing. In addition to the new algorithms, we show how the geometrical framework gives penetrating new insights allowing us to create, understand, and compare algorithms. The theory proposed here provides a taxonomy for numerical linear algebra algorithms that provide a top level mathematical view
Unsupervised Learning by Probabilistic Latent Semantic Analysis
 Machine Learning
, 2001
"... Abstract. This paper presents a novel statistical method for factor analysis of binary and count data which is closely related to a technique known as Latent Semantic Analysis. In contrast to the latter method which stems from linear algebra and performs a Singular Value Decomposition of cooccurren ..."
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Cited by 607 (4 self)
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Abstract. This paper presents a novel statistical method for factor analysis of binary and count data which is closely related to a technique known as Latent Semantic Analysis. In contrast to the latter method which stems from linear algebra and performs a Singular Value Decomposition of co
Probabilistic Latent Semantic Analysis
 In Proc. of Uncertainty in Artificial Intelligence, UAI’99
, 1999
"... Probabilistic Latent Semantic Analysis is a novel statistical technique for the analysis of twomode and cooccurrence data, which has applications in information retrieval and filtering, natural language processing, machine learning from text, and in related areas. Compared to standard Latent Sema ..."
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Cited by 756 (9 self)
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Semantic Analysis which stems from linear algebra and performs a Singular Value Decomposition of cooccurrence tables, the proposed method is based on a mixture decomposition derived from a latent class model. This results in a more principled approach which has a solid foundation in statistics. In order
Results 1  10
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