[go: up one dir, main page]

Akritas et al., 2007 - Google Patents

Computations in modules over commutative domains

Akritas et al., 2007

View PDF
Document ID
2770441725264932557
Author
Akritas A
Malaschonok G
Publication year
Publication venue
International Workshop on Computer Algebra in Scientific Computing

External Links

Snippet

This paper is a review of results on computational methods of linear algebra over commutative domains. Methods for the following problems are examined: solution of systems of linear equations, computation of determinants, computation of adjoint and …
Continue reading at wwwmayr.in.tum.de (PDF) (other versions)

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
    • G06F—ELECTRICAL DIGITAL DATA PROCESSING
    • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
    • G06F7/60—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers
    • G06F7/72—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers using residue arithmetic
    • G06F7/724—Finite field arithmetic
    • G06F7/726—Inversion; Reciprocal calculation; Division of elements of a finite field
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
    • G06F—ELECTRICAL DIGITAL DATA PROCESSING
    • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
    • G06F7/38—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation
    • G06F7/48—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices
    • G06F7/52—Multiplying; Dividing
    • G06F7/523—Multiplying only
    • G06F7/533—Reduction of the number of iteration steps or stages, e.g. using the Booth algorithm, log-sum, odd-even
    • G06F7/5332—Reduction of the number of iteration steps or stages, e.g. using the Booth algorithm, log-sum, odd-even by skipping over strings of zeroes or ones, e.g. using the Booth Algorithm
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
    • G06F—ELECTRICAL DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
    • G06F—ELECTRICAL DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
    • G06F—ELECTRICAL DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING; COUNTING
    • G06G—ANALOGUE COMPUTERS
    • G06G7/00—Devices in which the computing operation is performed by varying electric or magnetic quantities
    • G06G7/12—Arrangements for performing computing operations, e.g. operational amplifiers

Similar Documents

Publication Publication Date Title
Billey Kostant polynomials and the cohomology ring for G/B
Van Der Hoeven Newton’s method and FFT trading
Probert On the additive complexity of matrix multiplication
Akritas et al. Computations in modules over commutative domains
Zhou et al. Unimodular completion of polynomial matrices
Buchmann et al. On the computation of discrete logarithms in class groups
Zajac A new method to solve MRHS equation systems and its connection to group factorization.
Thompson et al. Division algebras and MRD codes from skew polynomials
Tasche et al. Worst and average case roundoff error analysis for FFT
Doliskani et al. Computing in degree 2 k-extensions of finite fields of odd characteristic
Cheng Algorithms for normal forms for matrices of polynomials and Ore polynomials
Fulman Stein's method, heat kernel, and traces of powers of elements of compact Lie groups
Spackman On the number and distribution of simultaneous solutions to diagonal congruences
Probert On the complexity of matrix multiplication
Mérai On the elliptic curve endomorphism generator
Malaschonok An algorithm for symbolic solving of differential equations and estimation of accuracy
Hillar et al. Polynomial recurrences and cyclic resultants
Chow et al. Shadowing of lattice maps
Brown et al. Cryptanalysis ofMAKE'
Malaschonok Parallel Laplace method with assured accuracy for solutions of differential equations by symbolic computations
González 2-divisibility in the Brown–Peterson [2k]-series
Cheng et al. On computing polynomial GCDs in alternate bases
Guillevic Faster individual discrete logarithms with the QPA and NFS variants
Beletsky Factorization of the Degree of Sphenic Polynomials over the Galois Fields of Arbitrary Characteristics
Anantharaman et al. Analysis of periodic feedback shift registers