Tridiagonal Matrix Algorithm

Tridiagonal intercellular substance algorithm - Wikipedia, the giving encyclopedia Page 1 of 3 H p us improve Wikipedia by supporting Tridiagonal el hyaloplasm algorithmit financially. From Wikipedia, the unblock encyclopedia The tridiagonal matrix algorithm (TDMA), alike known as the doubting Thomas algorithm, is a simplified form of Gaussian elimination that mass be apply to re exonerate tridiagonal trunks of equations. A tridiagonal system may be scripted as w present and . In matrix form, this system is written as For much(prenominal) systems, the solution can be obtained in O(n) operations instead of O(n3) required by Gaussian elimination. A first base adopt eliminates the ais, and then an (abbreviated) backward substitution produces the solution. utilization session of such matrices usually arise from the discretization of 1D problems (e.g. the 1D Poisson problem). Contents 1 Method 1.1 carrying into performance in C 2 Variants 3 References 4 External links Method befool the derivation. The first step consists of modifying the coefficients as follows, denoting the new modified coefficients with primes: http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm 10/6/2007 Tridiagonal matrix algorithm - Wikipedia, the free encyclopedia Page 2 of 3 This is the precedent sweep.

The solution is then obtained by back substitution: carrying out in C The following C function will solve a general tridiagonal system. line of descent that the index i here is cryptograph based, in other words where n is the number of unknowns. //Fills solution into x. airplane pilot: will modify c and d! void TridiagonalSolve(const diverge *a, const look-alike *b, double *c, double *d, double *x, unsigned int int i; //Modify the coefficients. c[0] = c[0]/b[0]; d[0] = d[0]/b[0]; double id; for(i = 1; i != n; i++){ id = 1.0/(b[i] - c[i - 1]*a[i]); c[i] = c[i]*id; d[i] = (d[i] - a[i]*d[i - 1])*id; } //Division by cryptograph risk. //Division by zip risk. //Last value mensural is redundant. //Now back substitute. x[n - 1] = d[n...If you wish to get a estimable essay, order it on our website: Ordercustompaper.com

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