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FIXED-POINT ALGORITHM;
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To find a solution to p = g(p) given an initial approximation p0: INPUT: initial approximation p0; tolerance TOL; maximum number of iterations N0. OUTPUT: approximate solution p or a message that the method fails.
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NEWTON-RAPHSON ALGORITHM;
4.0
Numerical calculations Algorithms: NEWTON-RAPHSON ALGORITHM in Math written by Pascal To find a solution to f(x) = 0 given an initial approximation p0: INPUT: initial approximation p0; tolerance TOL; maximum number of iterations NO. OUTPUT: approximate solution p or a message that the algorithm fails.
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SECANT ALGORITHM;
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Numerical calculations Algorithms: SECANT ALGORITHM in Math written by Pascal To find a solution to the equation f(x) = 0 given initial approximations p0 and p1: INPUT: initial approximations p0, p1; tolerance TOL; maximum number of iterations N0. OUTPUT: approximate solution p or a message that the algorithm fails.
saeed652 1 0
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METHOD OF FALSE POSITION;
no vote
Numerical calculations Algorithms: METHOD OF FALSE POSITION written by Pascal To find a solution to f(x) = 0 given the continuous function f on the interval [p0,p1], where f(p0) and f(p1) have opposite signs: INPUT: endpoints p0, p1; tolerance TOL; maximum number of iterations N0. OUTPUT: approximate solution p or a message that the algorithm fails.
saeed652 0 0
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STEFFENSEN'S ALGORITHM;
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Numerical calculations Algorithms: STEFFENSEN'S ALGORITHM written by Pascal To find a solution to g(x) = x given an initial approximation p0: INPUT: initial approximation p0; tolerance TOL; maximum number of iterations N0. OUTPUT: approximate solution p or a message that the method fails.
saeed652 0 0
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HORNER'S ALGORITHM ;
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Numerical calculations Algorithms: HORNER'S ALGORITHM in Math written by Pascal To evaluate the polynomial p(x) = a(n) * x ^ n + a(n-1) * x ^ (n-1) + ... + a(1) * x + a(0) and its derivative p'(x) at x = x0; INPUT: degree n; coefficients aa(0),aa(1),...,aa(n); value of x0. OUTPUT: y = p(x0), z = p'(x0).
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NEVILLE'S ITERATED INTERPOLATION ALGORITHM;
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Numerical calculations Algorithms: NEVILLE'S ITERATED INTERPOLATION ALGORITHM written by Pascal To evaluate the interpolating polynomial P on the (n+1) distinct numbers x(0), ..., x(n) at the number x for the function f: INPUT: numbers x(0),..., x(n) as XX(0),...,XX(N); number x; values of f as the first column of Q or may be computed if function f is supplied. OUTPUT: the table Q with P(x) = Q(N+1,N+1).
saeed652 1 0
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NEWTON'S INTERPOLATORY DIVIDED-DIFFERENCE FORMULA
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Numerical calculations Algorithms: NEWTON'S INTERPOLATORY DIVIDED-DIFFERENCE FORMULA ALGorithm BY PASCAL To obtain the divided-difference coefficients of the interpolatory polynomial P on the (n+1) distinct numbers x(0), x(1), ..., x(n) for the function f: INPUT: numbers x(0), x(1), ..., x(n); values f(x(0)), f(x(1)), ..., f(x(n)) as the first column Q(0,0), Q(1,0), ..., Q(N,0) OF Q, or may be computed if function f is supplied. OUTPUT: the numbers Q(0,0), Q(1,1), ..., Q(N,N) where P(x) = Q(0,0) + Q(1,1)*(x - x(0)) + Q(2,2)*(x - x(0))*
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HERMITE INTERPOLATION ALGORITHM;
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Numerical calculations Algorithms: HERMITE INTERPOLATION ALGORITHM TO OBTAIN THE COEFFICIENTS OF THE HERMITE INTERPOLATING POLYNOMIAL H ON THE (N+1) DISTINCT NUMBERS X(0), ..., X(N) FOR THE FUNCTION F: INPUT: NUMBERS X(0), X(1), ..., X(N); VALUES F(X(0)), F(X(1)), ..., F(X(N)) AND F'(X(0)), F'(X(1)), ..., F'(X(N)). OUTPUT: NUMBERS Q(0,0), Q(1,1), ..., Q(2N + 1,2N + 1) WHERE H(X) = Q(0,0) + Q(1,1) * ( X - X(0) ) + Q(2,2) * &nbs
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CLAMPED CUBIC SPLINE ALGORITHM;
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Numerical calculations Algorithms: CLAMPED CUBIC SPLINE ALGORITHM in Math Written by Pascal To construct the cubic spline interpolant S for the function f, defined at the numbers x(0) < x(1) < ... < x(n), satisfying S'(x(0)) = f'(x(0)) and S'(x(n)) = f'(x(n)): INPUT: n; x(0), x(1), ..., x(n); either generate A(I) = f(x(I)) for i = 0, 1, ..., n or input A(I) for I = 0, 1, ..., n; FPO = f'(x(0)) and FPN = f'(x(n)) are both input. OUTPUT: A(J), B(J), C(J), D(J) for J = 0, 1, ..., n - 1. NOTE: S(x) = A(J) + B(J) * ( x - x(J) ) + C(J) * ( x - x(J) )**2 +
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