How is the Lambert W function calculated?

The Lambert W function W(x) represents the solutions y of the equation y e y = x for any complex number x . For complex x, the equation has an infinite number of solutions y = lambertW(k,x) where k ranges over all integers. For all real x ≥ 0, the equation has exactly one real solution y = lambertW(x) = lambertW(0,x).

Is Newton’s method always applicable if the function f is twice continuously differentiable?

As such, Newton’s method can be applied to the derivative f ′ of a twice-differentiable function f to find the roots of the derivative (solutions to f ′(x) = 0), also known as the critical points of f.

What is the value of Lambert W?

In mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse relation of the function f(w) = wew, where w is any complex number and ew is the exponential function.

Is Lambert W function Elementary?

can be solved for y only if x ≥ −1e; we get y = W0(x) if x ≥ 0 and the two values y = W0(x) and y = W−1(x) if − 1e ≤ x < 0. The Lambert W relation cannot be expressed in terms of elementary functions.

Why does Newton’s method fail?

Newton’s method will fail in cases where the derivative is zero. When the derivative is close to zero, the tangent line is nearly horizontal and hence may overshoot the desired root (numerical difficulties). Solution: Try another initial point.

What are the drawbacks of Newton Raphson method?

Disadvantages of Newton Raphson Method

• It’s convergence is not guaranteed.
• Division by zero problem can occur.
• Root jumping might take place thereby not getting intended solution.
• Inflection point issue might occur.
• Symbolic derivative is required.
• In case of multiple roots, this method converges slowly.

How do you find the number of solutions in Lambert W function?

Lambert W Function. The Lambert W function W(x) represents the solutions y of the equation for any complex number x. For complex x, the equation has an infinite number of solutions y = lambertW(k,x) where k ranges over all integers. For all real x ≥ 0, the equation has exactly one real solution y = lambertW(x) = lambertW(0,x).

What is the Lambert W function for complex X?

The Lambert W function W (x) represents the solutions y of the equation y e y = x for any complex number x. For complex x, the equation has an infinite number of solutions y = lambertW (k,x) where k ranges over all integers.

What are the applications of the Lambert W relation?

The Lambert W relation cannot be expressed in terms of elementary functions. It is useful in combinatorics, for instance, in the enumeration of trees.

Can lambertw return a floating-point result?

Depending on its arguments, lambertw can return floating-point or exact symbolic results. Compute the Lambert W functions for these numbers. Because the numbers are not symbolic objects, you get floating-point results. Compute the Lambert W functions for the numbers converted to symbolic objects.