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Second approximation
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Second approximation
The regula falsi is an approximation method for determining the solutions of equations for which the application of exact methods for calculation do not exist or are too complicated in their handling.
This applies, for example, to the determination of the solutions of equations of third or higher degree with one unknown, for root equations, exponential equations, logarithmic equations and trigonometric equations – a website that does your homework . But also the calculation of curvilinear bounded surfaces or curvilinear bounded bodies usually requires the use of approximation methods.
A basic idea of the approximation methods for the determination of the solutions of equations consists of converting the equation into a function equation, so that the variable of the equation appears as a variable of the function – matlab homework help . The zero of this function is then searched for. Instead of the equation p(x) = 0, the function f(x) = p(x) is considered. This “searching” means to improve step by step an approximate solution found e.g. by trying with special values or by estimation or to reduce systematically an interval in which the solution lies.
A method for zero determination used since the Middle Ages is known as regula falsi (rule of the wrong value) or secant approximation method.
To determine the solutions of the equation p(x) = 0, the function f(x) = p(x) is considered. In the interval [x0;x1] then at least one zero exists, if the function is continuous in the interval and has different signs at the interval ends – excel homework help . The curve points at the ends of the interval are connected by a straight line (the secant) and the intersection of this straight line with the x-axis is considered as an improvement of the interval. The initial interval is thus divided into two smaller intervals. With the partial interval, in which now the zero lies, the iteration (approximation) is then continued.
The intersection of the secant with the x-axis is determined by applying the ray theorem. The calculated value is considered as an improved solution.
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