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  2. Step function - Wikipedia

    en.wikipedia.org/wiki/Step_function

    As such, the step functions form an algebra over the real numbers. A step function takes only a finite number of values. If the intervals , for =,, …, in the above definition of the step function are disjoint and their union is the real line, then () = for all . The definite integral of a step function is a piecewise linear function.

  3. Heaviside step function - Wikipedia

    en.wikipedia.org/wiki/Heaviside_step_function

    The Heaviside step function, or the unit step function, usually denoted by H or θ (but sometimes u, 1 or ๐Ÿ™), is a step function named after Oliver Heaviside, the value of which is zero for negative arguments and one for positive arguments. Different conventions concerning the value H(0) are in use.

  4. Step potential - Wikipedia

    en.wikipedia.org/wiki/Step_potential

    In quantum mechanics and scattering theory, the one-dimensional step potential is an idealized system used to model incident, reflected and transmitted matter waves.The problem consists of solving the time-independent Schrödinger equation for a particle with a step-like potential in one dimension.

  5. Conjugate gradient method - Wikipedia

    en.wikipedia.org/wiki/Conjugate_gradient_method

    A comparison of the convergence of gradient descent with optimal step size (in green) and conjugate vector (in red) for minimizing a quadratic function associated with a given linear system. Conjugate gradient, assuming exact arithmetic, converges in at most n steps, where n is the size of the matrix of the system (here n = 2).

  6. Euler method - Wikipedia

    en.wikipedia.org/wiki/Euler_method

    This differs from the (standard, or forward) Euler method in that the function is evaluated at the end point of the step, instead of the starting point. The backward Euler method is an implicit method , meaning that the formula for the backward Euler method has y n + 1 {\displaystyle y_{n+1}} on both sides, so when applying the backward Euler ...

  7. Numerical methods for ordinary differential equations

    en.wikipedia.org/wiki/Numerical_methods_for...

    The step size is =. The same illustration for = The midpoint method converges faster than the Euler method, as .. Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs).

  8. Step response - Wikipedia

    en.wikipedia.org/wiki/Step_response

    The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory , step response is the time behaviour of the outputs of a general system when its inputs change from zero to one in a very short time.

  9. Smoothstep - Wikipedia

    en.wikipedia.org/wiki/Smoothstep

    A plot of the smoothstep(x) and smootherstep(x) functions, using 0 as the left edge and 1 as the right edgeSmoothstep is a family of sigmoid-like interpolation and clamping functions commonly used in computer graphics, [1] [2] video game engines, [3] and machine learning.

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