A single hidden layer feedforward network with only one neuron in
... Chui and Li [6] proved that a single hidden layer network with a continuous sigmoidal activation function having integer weights and thresholds can approximate an arbitrary continuous function on a compact subset of R. Ito [18] established a density result for continuous functions on a compact subse ...
... Chui and Li [6] proved that a single hidden layer network with a continuous sigmoidal activation function having integer weights and thresholds can approximate an arbitrary continuous function on a compact subset of R. Ito [18] established a density result for continuous functions on a compact subse ...
Linear Functions
... A linear function of a real variable x is given by y = f(x) = ax + b, a and b are constant real numbers. The graph of a linear equation is a straight line. The number a is called the slope of the function and the number b is called the y-intercept. The y-intercept is the value of the function when x ...
... A linear function of a real variable x is given by y = f(x) = ax + b, a and b are constant real numbers. The graph of a linear equation is a straight line. The number a is called the slope of the function and the number b is called the y-intercept. The y-intercept is the value of the function when x ...
Fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral.The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that the definite integration of a function is related to its antiderivative, and can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions.The second part of the theorem, sometimes called the second fundamental theorem of calculus, is that the definite integral of a function can be computed by using any one of its infinitely-many antiderivatives. This part of the theorem has key practical applications because it markedly simplifies the computation of definite integrals.