منابع مشابه
New algorithms for relaxed multiplication
In previous work, we have introduced the technique of relaxed power series computations. With this technique, it is possible to solve implicit equations almost as quickly as doing the operations which occur in the implicit equation. Here almost as quickly means that we need to pay a logarithmic overhead. In this paper, we will show how to reduce this logarithmic factor in the case when the cons...
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Strassen’s and Winograd’s algorithms for n × n matrix multiplication are investigated and compared with the normal algorithm. The normal algorithm requires n3 + O(n2) multiplications and about the same number of additions. Winograd’s algorithm almost halves the number of multiplications at the expense of more additions. Strassen’s algorithm reduces the total number of operations to O(n2.82) by ...
متن کاملRelaxed Multiplication Using the Middle Product
In previous work, we have introduced the technique of relaxed power series computations. With this technique, it is possible to solve implicit equations almost as quickly as doing the operations which occur in the implicit equation. In this paper, we present a new relaxed multiplication algorithm for the resolution of linear equations. The algorithm has the same asymptotic time complexity as ou...
متن کاملNew Algorithms for Constant Coefficient Multiplication in Custom Hardware
Multiplying by known constants is a common operation in many digital signal processing (DSP) algorithms. High performance DSP systems are implemented in custom hardware, in which the designer has the ability to choose which logic elements will be used to perform the computation. By exploiting the properties of binary multiplication, it is possible to realize constant multiplication with fewer l...
متن کاملNew Modular Multiplication Algorithms for Fast Modular Exponentiation
A modular exponentiation is one of the most important operations in public-key cryptography. However, it takes much time because the modular exponen-tiation deals with very large operands as 512-bit integers. The modular exponentiation is composed of repetition of modular multiplications. Therefore, we can reduce the execution time of it by reducing the execution time of each modular multiplica...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2007
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2007.04.004