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On the Additive Complexity of Matrix Multiplication
SIAM Journal on Computing, 1976A graph-theoretic model is introduced for bilinear algorithms. This facilitates in particular the investigation of the additive complexity of matrix multiplication. The number of additions/subtractions required for each of the problems defined by symmetric permutations on the dimensions of the matrices are shown to differ conversely as the size of each
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Proceedings of the 2005 European Conference on Circuit Theory and Design, 2005., 2006
Multiple constant multiplication (MCM) has been an active research area for the last decade. Most work so far have only considered the number of additions to realize a number of constant multiplications with the same input. In this work, we consider the number of full and half adder cells required to realize those additions, and a novel complexity ...
Kenny Johansson +2 more
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Multiple constant multiplication (MCM) has been an active research area for the last decade. Most work so far have only considered the number of additions to realize a number of constant multiplications with the same input. In this work, we consider the number of full and half adder cells required to realize those additions, and a novel complexity ...
Kenny Johansson +2 more
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Multiple complexes of thrombin and heparin
Biochimica et Biophysica Acta (BBA) - Protein Structure and Molecular Enzymology, 1986Fluorescence polarization has been used to study the interaction of thrombin and heparin, and the catalysis by heparin of the combination of thrombin and antithrombin. At low ionic strength (20 mM Tris, pH 7.4), the addition of heparins of known molecular weights to thrombin led to the formation of large complexes (defined as 'complex 1').
J R, Evington +3 more
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Circuit Complexity and Multiplicative Complexity of Boolean Functions
2010In this note, we use lower bounds on Boolean multiplicative complexity to prove lower bounds on Boolean circuit complexity. We give a very simple proof of a 7n/3 - c lower bound on the circuit complexity of a large class of functions representable by high degree polynomials over GF(2). The key idea of the proof is a circuit complexity measure assigning
Arist Kojevnikov, Alexander S. Kulikov
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Lower bounds for the multiplicative complexity of matrix multiplication
Computational Complexity, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Complex aggregation at multiple granularities
1998Datacube queries compute simple aggregates at multiple granularities. In this paper we examine the more general and useful problem of computing a complex subquery involving multiple dependent aggregates at multiple granularities. We call such queries “multi-feature cubes.” An example is “Broken down by all combinations of month and customer, find the ...
Kenneth A. Ross +2 more
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Parallel complexity of matrix multiplication
J. Supercomput., 2003Matrix multiplication is a kernel of many numerical algorithms, thus finding efficient and parallel solution to this problem is one of the most important topics in scientific computing. In this paper, the parallel complexity of multiplying two matrices (using the standard row/column method) on parallel distributed-memory computers is studied.
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The multiplicative complexity of boolean functions
1989Let the multiplicative complexity L(f) of a boolean function f be the minimal number of Λ-gates (with two entries) that are sufficient to evaluate f by circuits over the basis Λ,⊕,1. We relate L(f) with the dimension of the dual domain D(f); D(f) is the minimal linear space of linear boolean forms such that f modulo linear functions can be written as a
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Performance engineering for real and complex tall & skinny matrix multiplication kernels on GPUs
International Journal of High Performance Computing Applications, 2021Gerhard Wellein +2 more
exaly
On the complexity of quaternion multiplication
Information Processing Letters, 1975openaire +2 more sources