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CROUT FACTORIZATION FOR TRIDIAGONAL LINEAR SYSTEMS
no vote
% % To solve the n x n linear system % % E1:  A(1,1) X(1) + A(1,2) X(2)                  = A(1,n+1) % E2:  A(2,1) X(1) + A(2,2) X(2) + A(2,3) X(3)    = A(2,n+1) % : % . % E(n):          A(n,n-1) X(n-1) + A(n,n) X(n)    = A(n,n+1) % % INPUT:   the dimension n; the entries of A. % % OUTPUT:  the solution X(1), ..., X(N).
s6531
2020-01-15
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CHOLESKI'S ALGORITHM
no vote
% % To factor the positive definite n by n matrix A into LL**T, % where L is lower triangular. % % INPUT:   the dimension n; entries A(I,J), 1<=I, J<=n of A. % % OUTPUT:  the entries L(I,J), 1<=J<=I, 1<=I<=n of L. %
s6531
2020-01-15
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1
LDL^t ALGORITHM
no vote
% % To factor the positive definite n by n matrix A into LDL**T, % where L is a lower triangular matrix with ones along the diagonal % and D is a diagonal matrix with positive entries on the % diagonal. % % INPUT:   the dimension n; entries A(I,J), 1<=I, J<=n of A. % % OUTPUT:  the entries L(I,J), 1<=J<I, 1<=I<=N of L and D(I), %          1<=I<=n of D.
s6531
2020-01-15
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DIRECT FACTORIZATION ALGORITHM
no vote
% % To factor the n by n matrix A = (A(I,J)) into the product of the % lower triangular matrix L = (L(I,J)) and the upper triangular % matrix U = (U(I,J)), that is A = LU, where the main diagonal of % either L or U consists of all ones: % % INPUT:   dimension n; the entries A(I,J), 1<=I, J<=n, of A; %          the diagonal L(1,1), ..., L(N,N) of L or the diagonal %          U(1,1), ..., U(N,N) of U. % % OUTPUT:  the entries L(I,J), 1<=J<=I, 1<=I<=n of L and the entries %          U(I,J), I<=J<=n, 1<=I<=n of U.
s6531
2020-01-15
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GAUSSIAN ELIMINATION WITH SCALED PARTIAL PIVOTING
no vote
% To solve the n by n linear system % % E1:  A(1,1) X(1) + A(1,2) X(2) +...+ A(1,n) X(n) = A(1,n+1) % E2:  A(2,1) X(1) + A(2,2) X(2) +...+ A(2,n) X(n) = A(2,n+1) %   : %   . % EN:  A(n,1) X(1) + A(n,2) X(2) +...+ A(n,n) X(n) = A(n,n+1) % % INPUT:   number of unknowns and equations n; augmented %          matrix A = (A(I,J)) where 1<=I<=n and 1<=J<=n+1. % % OUTPUT:  solution x(1), x(2),...,x(n) or a message that the
s6531
2020-01-15
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1
GAUSSIAN ELIMINATION WITH BACKWARD SUBSTITUTION AL
no vote
% % To solve the n by n linear system % % E1:  A(1,1) X(1) + A(1,2) X(2) +...+ A(1,n) X(n) = A(1,n+1) % E2:  A(2,1) X(1) + A(2,2) X(2) +...+ A(2,n) X(n) = A(2,n+1) % : % . % EN:  A(n,1) X(1) + A(n,2) X(2) +...+ A(n,n) X(n) = A(n,n+1) % % INPUT:   number of unknowns and equations n; augmented %          matrix A = (A(I,J)) where 1<=I<=n and 1<=J<=n+1. % % OUTPUT:  solution x(1), x(2),...,x(n) or a message that the %          linear system has no unique solution.
s6531
2020-01-15
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1
MULLER'S ALGORITHM
no vote
%  % To find a solution to f(x) = 0 given three approximations x0, x1  % and x2:  %  % INPUT:  x0,x1,x2; tolerance TOL; maximum number of iterations NO.  %  % OUTPUT: approximate solution p or message of failure.  %  % This implementation allows for a switch to complex arithmetic.  % The coefficients are stored in the vector A, so the dimension  % of A may have to be changed.
s6531
2020-01-15
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STEFFENSEN'S ALGORITHM
no vote
%  % 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.
s6531
2020-01-15
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METHOD OF FALSE POSITION ALGORITHM
no vote
%  % 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
s6531
2020-01-15
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SECANT ALGORITHM
no vote
%  % To find a solution to the equation f(x) = 0  % given initial approximations p0 and p1:  %  % INPUT:   initial approximation p0, p1; tolerance TOL;  %          maximum number of iterations N0.  %  % OUTPUT:  approximate solution p or  %          a message that the algorithm fails.
s6531
2020-01-15
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