Residue Arithmetic Algorithms for Exact Computation of<i>g</i>-Inverses of Matrices

Rao, T. M.; Subramanian, K. G.; Krishnamurthy, E. V.

doi:10.1137/0713017

Cited by 40 publications

(16 citation statements)

References 6 publications

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“…The infinite series converges to the rational number in the P-adic norm [3]. We decode P-adic series by Dixon algorithm and the Extended Euclidean algorithm [5] as in Fig. 5.…”

Section: Implementation Of Dixon-krishnamurthy Algorithmmentioning

confidence: 99%

“…The notations p x and p X will be used to denote the residue of an integer x and matrix X with respect to positive integer p , via mod p [5].…”

Section: B Krishnamurthy Algorithmmentioning

confidence: 99%

“…NTL written by Shoup [4] is the one we have picked as a computational vehicle for comparison with the P-adic Exact Scientific Computational Library (ESCL) we have been developing. Our alternative approach is to represent all rational numbers in terms of a set of residues with respect to a prime number and its powers, called a P-adic number system since the P-adic arithmetic has many attractive features [5]. Algorithms of matrix operations are developed with rational numbers by representing numerator and denominator with arbitrary length integers, and for linear computation with modulo arithmetic using the P-adic number system.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Efficient Algorithms and Implementation for Error-Free Computation Using P-adic

Zhao

Lü

2011

2011 First ACIS/JNU International Conference on Computers, Networks, Systems and Industrial Engineering

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Our research team including graduate students both in Computer Science and Mathematics has been developing P-adic Exact Scientific Computational Library (ESCL) for rational matrix operations. The effort has been focusing on converting all rational number operations to integer calculation, and fully taking the advantage of fast integer multiplication of modern computer architectures [1]. By properly selecting prime numbers as the bases and practically choosing the length r for P-adic expansion of rational numbers, we have shown some promising results for large matrix operations, such as matrix multiplication and inverse. Dixon algorithm [2] and his improved version, we call it GeneralizedDixon (or Dixon-Krishnamurthy) algorithm, which combines Dixon algorithm with Krishnamurthy algorithm [3], has been developed, which can be extended to various matrix computations.

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“…The infinite series converges to the rational number in the P-adic norm [3]. We decode P-adic series by Dixon algorithm and the Extended Euclidean algorithm [5] as in Fig. 5.…”

Section: Implementation Of Dixon-krishnamurthy Algorithmmentioning

confidence: 99%

“…The notations p x and p X will be used to denote the residue of an integer x and matrix X with respect to positive integer p , via mod p [5].…”

Section: B Krishnamurthy Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient Algorithms and Implementation for Error-Free Computation Using P-adic

Zhao

Lü

2011

2011 First ACIS/JNU International Conference on Computers, Networks, Systems and Industrial Engineering

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“…One of the aspects of this problem is to predict the required word length. Rao (1976) [11] and Dixon (1982) [8] both gave ways to predict the length of the P-adic expansion for specific matrix calculation. But for some cases, it is hard to predict properly when the matrix calculation process is overly complex.…”

Section: Introductionmentioning

confidence: 99%

A method for Hensel code overflow detection

Lü

Sjogren

2012

SIGAPP Appl. Comput. Rev.

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Hensel code was originally defined by Krishnamurthy, Rao and Subramanian [1], which was developed from the P-adic number system first proposed by Hensel in 1900s. The purpose was to realize exact computation for rational numbers. The Hensel code arithmetic has been well developed [1, 2, 3], but the problem of detecting Hensel code overflow and underflow has not been properly addressed [3]. In this paper, we proposed a method for Hensel code overflow detection. The method can realize overflow detection by the prime p and the Hensel code itself. Using this method, a few digits of the Hensel code will be sacrificed.

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“…[54] A{1, 2, 3} = W 1 (QW 1 ) −1 (P * P ) −1 P * = Q −1 r P † [54] A{1, 2, 4} = Q * (QQ * ) −1 (W 2 P ) −1 W 2 = Q † P −1 l [54] A # = P (QP ) −2 Q, gde P −1 l predstavlja levi inverz matrice P , a Q −1 r desni inverz matrice Q [43,44].…”

Section: Teorema 113mentioning

confidence: 99%

Computation of generalized inveses

Tasić¹

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Residue Arithmetic Algorithms for Exact Computation ofg-Inverses of Matrices

Cited by 40 publications

References 6 publications

Efficient Algorithms and Implementation for Error-Free Computation Using P-adic

Efficient Algorithms and Implementation for Error-Free Computation Using P-adic

A method for Hensel code overflow detection

Computation of generalized inveses

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