Numerical Solutions of Transcendental Equations and System of Linear Equations and Expansion of Function.
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See all →- What is a transcendental equation and how do I locate an interval containing its root? In one line A transcendental equation contains non-polynomial functions such as e^x , log x , sin x (e.g. x=cos x ); we locate a root by fin... 1
- How does the Newton–Raphson method find a root of f(x) = 0 and why does it work? In one line Newton–Raphson improves a guess x_n by sliding down the tangent line to the x -axis: x_(n+1)=x_n-f(x_n)/f'(x_n) . Explained simp... 1
- How does the Regula Falsi (false position) method find a root, and how is it different from Newton–Raphson? In one line Regula Falsi joins the points (a,f(a)) and (b,f(b)) on opposite sides of the axis by a straight chord and takes where the chord... 1
- How do I derive Newton–Raphson iterative formulas for square roots, cube roots and reciprocals? In one line Write the required number as the root of a simple equation, such as x²-N=0 for sqrt N , and apply x_(n+1)=x_n-f(x_n)/f'(x_n) to... 1
- How does the Gauss–Jacobi iteration method solve a system of linear equations? In one line Gauss–Jacobi rewrites each equation to make one unknown the subject, then repeatedly substitutes the previous round's values int... 1
- How is the Gauss–Seidel method different from Gauss–Jacobi, and why does it converge faster? In one line Gauss–Seidel is Jacobi with one change: each newly computed value is used immediately in the following equations of the same ite... 1