Backward substitution algorithm
[DOC File]Assignment #3 - University of Windsor
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Now, we need to compute d = e-1 mod f(n) by using backward substitution of GCD algorithm: According to GCD: 20 = 7 * 2 + 6 . 7 = 6 * 1 + 1. 6 = 1 * 6 + 0 . Therefore, we have: 1 = 7 – 6 = 7 – (20 – 7 * 2) = 7 – 20 + 7 * 2 = -20 + 7 * 3 . Hence, we get d = e-1 mod f(n) = e-1 mod 20 = 3 mod 30 = 3 . So, the public key is {7, 33} and the private key is {3, 33}, RSA encryption and ...
[DOC File]Numerical Analysis
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061.C* - Gaussian Elimination with Backward Substitution Algorithm 6.1. 061B.C* - Gaussian Elimination with Backward Substitution Algorithm 6.1B (with rounding) 061C1.C* - Gauss-Jordan Method Algorithm 6.1C1. 061C2.C* - Gauss-Jordan Method (with rounding) Algorithm 6.1C2. 061D1.C* - Gaussian-Elimination - Gauss-Jordan Hybrid Method Algorithm 6.1D1 . 061D2.C* - Gaussian …
[DOC File]Week .tr
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Algorithm complexity (Best-case, Worst-case, Average complexity) Asymptotic analysis (Growth rate, Aymptotic notation, Comparison of growth rates) Analysis of example algorithms. Interpolation (θ-invariant under scaling, Scale invariant classes) Stable, in-place, on-line algorithms. Adjacent-key comparison-based algorithms. Recurrence relations (Forward substitution, Backward substitution ...
[DOC File]NATIONAL UNIVERSITY
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Bisection algorithm. Method of false position. Fixed point iteration. Newton-Raphson method. Convergence analysis. Interpolation and polynomial approximation: Newton’s forword and bacword, Newton’s general formula.Taylor polynomials. Lagrange polynomial. Iterated interpolation. Extrapolation. Differentiation and Integration: Numerical differentiation. Richardson’s extrapolation. Elements ...
[DOC File]Fast Solving of Rank Deficient Least Square Systems
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We first define the generalization of the backward substitution method for computing generalized inverses of generalized Cholesky factors as they are defined in Theorem 2. The computational complexity of the generalized algorithm is the same as that of the original backward substitution method (). The algorithm is designed to solve in the following equation: , (9) where is a diagonal matrix ...
[DOC File]CSCE 340/840
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Use forward and backward substitution to complete the solution process. Note that you will need to reference elements of A as A(p(i),j) in the forward and backward algorithms. In the forward and backward solution process use at most two vectors, i.e., y, b, x. The solution process is to solve Ly = b followed by Ux = y. Your factorization, forward, and backward algorithms (subprograms) should ...
[DOC File]Notes 10: Conductor sizing & an example
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Given the L and U factors, we need to only perform forward and backward substitution for each different right-hand-side. Algorithm: I indicated the power flow algorithm is exactly the same as in the full-Newton, but there is a minor difference in that Step 3 (page 7) and Step 4 (page 8) can be alternated, as follows: Step 3a: Compute mismatch of using and . Step 4a: Solve eq. (46) for . Step ...
[DOC File]Section 4 - Baylor University
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Gaussian Elimination and Backward Substitution. Gaussian elimination is the most common method for solving bus voltages in a circuit for which KCL equations have been written in the form . Of course, direct inversion can be used, where, but direct inversion for large matrices is computationally prohibitive or, at best, inefficient. The objective of Gaussian elimination is to reduce the Y ...
[DOC File]Notes 10: Conductor sizing & an example
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backward substitution. Consideration of the pattern of calculation introduced by eqs. (14)-(16) suggests a generalized formula for forward substitution, useful for computer programming, as follows: (17) where n is the dimension of the matrix. Factorization using Crout algorithm. So we see that if we have L and U, we can solve A x=b for x. So natural question at this point is: How to find L and ...
[DOC File]Implementing Finite Difference Solvers for the BS-PDE
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The backward Euler method uses the known value at u(x,-) to set up an equation involving the three u-values u(x-x,), u(x,), and u(x+x,).
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