A Fast Algorithm for Gaussian Elimination over GF(2) and Its Implementation on the GAPP
نویسندگان
چکیده
A fast algori thm for Gaussian eliminat ion over GF(2) is proposed. The proposed algorithm employs binary search technique to locate l s along the colum ns of the large binary matrix being triangular ized. T he algori thm requires 2m 2 + m log211 2m bit operations to triang ularize an II X m matrix on a bit-array with 11 processors and m + 2 + l"log2nl bits of vertica l memory per processor . Deta ils of an implementation on the Geometr ic Arithmetic Paralle l Processor arc also presented. © 1991 Academic
منابع مشابه
SMITH - A Parallel Hardware Architecture for fast Gaussian Elimination over GF(2)
This paper presents a hardware-optimized variant of the well-known Gaussian elimination over GF(2) and its highly efficient implementation. The proposed hardware architecture, we call SMITH1, can solve any regular and (uniquely solvable) overdetermined linear system of equations (LSE) and is not limited to matrices of a certain structure. Besides solving LSEs, the architecture at hand can also ...
متن کاملA compact algorithm for Gaussian elimination over GF(2) implemented on highly parallel computers
Gaussian elimination over GF(2) is used in a number of applications including the factorisation of large integers. The boolean nature of arithmetic in GF(2) makes the task well suited to highly parallel bit-organised computers. A program to work with up to 4096X4096 matrices has been developed for the ICL-DAP. A method has been developed that needs no extra storage to store the history of the e...
متن کاملEfficient implementation of low time complexity and pipelined bit-parallel polynomial basis multiplier over binary finite fields
This paper presents two efficient implementations of fast and pipelined bit-parallel polynomial basis multipliers over GF (2m) by irreducible pentanomials and trinomials. The architecture of the first multiplier is based on a parallel and independent computation of powers of the polynomial variable. In the second structure only even powers of the polynomial variable are used. The par...
متن کاملSolving Homogeneous Linear Equations over Gf(2) via Block Wiedemann Algorithm
We propose a method of solving large sparse systems of homogeneous linear equations over GF(2), the field with two elements. We modify an algorithm due to Wiedemann. A block version of the algorithm allows us to perform 32 matrix-vector operations for the cost of one. The resulting algorithm is competitive with structured Gaussian elimination in terms of time and has much lower space requiremen...
متن کاملA Fast and Efficient On-Line Harmonics Elimination Pulse Width Modulation for Voltage Source Inverter Using Polynomials Curve Fittings
The paper proposes an algorithm to calculate the switching angles using harmonic elimination PWM (HEPWM) scheme for voltage source inverter. The algorithm is based on curve fittings of a certain polynomials functions. The resulting equations require only the addition and multiplication processes; therefore, it can be implemented efficiently on a microprocessor. An extensive angle error analysis...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Parallel Distrib. Comput.
دوره 13 شماره
صفحات -
تاریخ انتشار 1991