Punktpunktintegratsioon

Punktpunktintegratsioon, often abbreviated as PPI, is a mathematical technique used to approximate the integral of a function by summing the function's values at specific points. This method is a fundamental concept in numerical analysis and forms the basis for many more advanced integration techniques. The core idea is to divide the area under the curve of a function into a series of smaller, manageable shapes, such as rectangles or trapezoids, and then sum the areas of these shapes.

The simplest form of punktpunktintegratsioon is the rectangle rule, where the function's value at a single point within each subinterval is used to determine the height of a rectangle. Other common methods include the midpoint rule, where the function's value at the midpoint of each subinterval is used, and the trapezoidal rule, which approximates the area under the curve in each subinterval using a trapezoid.

The accuracy of punktpunktintegratsioon increases as the number of subintervals used in the approximation increases. This is because a larger number of smaller shapes can more closely follow the contour of the original function. For practical applications, punktpunktintegratsioon is essential when an exact analytical solution for an integral is difficult or impossible to obtain, or when dealing with data that is only available at discrete points.