Methods for solving PDEs typically exploit the sparsity of the residual Jacobian; the deflated Jacobian is dense, but we devise an efficient preconditioner for the dense deflated systems via the Sherman–Morrison formula. Finally, we demonstrate its widespread applicability on several problems of ...
To improve the discriminant capability of features, biological domain knowledge, such as pathways are more often referred to during cancer classification to give more robust and generalizable results12,13,14,15,16,17,18,19. Pathways, being a series of interactions among molecules (including genes,...
If the solutions to a quadratic equation are imaginary numbers, it means that the equation has no real solutions. This occurs when the discriminant (b^2 - 4ac) is negative. The solutions will involve the imaginary unit i and will be in the form a + bi and a - bi. ...
Then, an investigation of its real roots is done by analyzing the discriminant sequence and extensive numerical computations.doi:10.1016/j.jsc.2021.06.002Dehbi LydiaZeng ZhenbingYang LuJournal of Symbolic Computation
"""dx, dy = p2.x - p1.x, p2.y - p1.y a = dx**2+ dy**2b =2* (dx * (p1.x - center.x) + dy * (p1.y - center.y)) c = (p1.x - center.x)**2+ (p1.y - center.y)**2- radius**2discriminant = b**2-4* a * cassert(discriminant >0),'N...