A New Variant of Gaussian Elimination

Algorithm 576: A FORTRAN Program for Solving Ax = b [F4]

“…, 0] T is the approximate solution obtained by back substitution in the first k equations. Then the right-hand sides of the last n -k equations are the nonzero components of the residual vector r (k) = b -Ax(k); this is proved in [1]. Our pivoting strategy thus chooses the equation with the absolutely largest residual as the next equation to be eliminated, and the (k + 1)th pivot is then selected as the absolutely largest of the n -k coefficients on the left-hand side of the chosen equation.…”

“…Given any n × n system of linear equations A x = b (1) and a n u m b e r e, the algorithm calculates the solution x to (1), if ~ _< O, or an approximation solution x (k) satisfying…”

“…Furthermore, if A appears to be singular, an approximate solution to (1) is still determined, although it does not satisfy (2). The algorithm consists of Gaussian elimination combined with a n e w pivoting strategy based on the following fact.…”

نمذجة معدل انتشار الفيروسات باستخدام الأساليب الحديثة لتحليل الأبعاد

“…There are already many references utilizing matrices in the derivation of dimensionless products [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] . We accomplish that derivation herein via the well-known Gauss-Jordan procedure or algorithm [40][41][42][43][44][45][46] . Our method distinguishes itself by making the most of this algorithm, and exploiting many of its inherent strengths in innovative and unprecedented ways.…”