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This x-intercept will typically be a better approximation to the original function's root than the first guess, and the method can be iterated. x n+1 is a better approximation than x n for the root x of the function f (blue curve) If the tangent line to the curve f(x) at x = x n intercepts the x-axis at x n+1 then the slope is
A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of an iterative method or a method of successive approximation. An iterative method is called convergent if the corresponding sequence converges for given ...
A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...
The successive-approximation register is initialized with 1 in the most significant bit (MSB) and zeroes in the lower bits. The register's code is fed into the DAC, which provides an analog equivalent of its digital code (initially 1 / 2 V ref ) to the comparator for comparison with the sampled input voltage.
Successive approximation also may refer to: Successive approximation ADC , analog-to-digital-conversion method appropriate for signal processing Shaping , behaviorist-psychology strategy of conditioning subtle behaviors only after conditioning gross behaviors
The geometric interpretation of Newton's method is that at each iteration, it amounts to the fitting of a parabola to the graph of () at the trial value , having the same slope and curvature as the graph at that point, and then proceeding to the maximum or minimum of that parabola (in higher dimensions, this may also be a saddle point), see below.
Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation. An alternative method is to use techniques from calculus to obtain a series expansion of the ...
A successive-approximation ADC uses a comparator and a binary search to successively narrow a range that contains the input voltage. At each successive step, the converter compares the input voltage to the output of an internal digital-to-analog converter (DAC) which initially represents the midpoint of the allowed input voltage range. At each ...