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EEE244 Numerical Methods in Engineering
EEE244 Numerical Methods in Engineering

... • Two matrices are considered equal if and only if every element in the first matrix is equal to every corresponding element in the second. This means the two matrices must be the same size. • Matrix addition and subtraction are performed by adding or subtracting the corresponding elements. This req ...
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... appearing in the third row and first column. A matrix A may also be denoted as [aij], where aij denotes the general element of A appearing in the ith row and jth column. A matrix having r rows and с columns has order (or size) "r by c," usually written rc. Two matrices are equal if they have the sa ...
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continued fraction method - McMaster Computing and Software

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FMROT.pdf

... step 1.5. B proves to A that B knows a square root of y mod m, without giving A any ideas which square root B knows. Step 1.5 requires a (sub)protocol to be performed which is very interesting in its own right. We now describe that protocol. The properties possessed by the subprotocol will become mo ...
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Hidden Markov Models

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... The Greatest Common Divisor of Two Numbers Recall that the greatest common divisor of two numbers, denoted as gcd(a,b), is the largest number that divides a and b evenly with no remainder. For example, gcd(10, 20). = 10 and gcd(72, 108)=36. Previously, we saw a method to find the gcd that involved m ...
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Ch.6 Fixed-Point vs. Floating Point

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Computing the Digits in π

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Algorithms and Data Structures

... Divide: If the input size is too large to deal with in a straightforward manner, divide the problem into two or more disjoint subproblems Conquer: Use divide and conquer recursively to solve the subproblems Combine: Take the solutions to the subproblems and “merge” these solutions into a solution fo ...
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Factorization of polynomials over finite fields

In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them.The case of the factorization of univariate polynomials over a finite field, which is the subject of this article, is especially important, because all the algorithms (including the case of multivariate polynomials over the rational numbers), which are sufficiently efficient to be implemented, reduce the problem to this case (see Polynomial factorization). It is also interesting for various applications of finite fields, such as coding theory (cyclic redundancy codes and BCH codes), cryptography (public key cryptography by the means of elliptic curves), and computational number theory.As the reduction of the factorization of multivariate polynomials to that of univariate polynomials does not have any specificity in the case of coefficients in a finite field, only polynomials with one variable are considered in this article.
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