Approximation
Object which deals with the approximations of function values.
Attributes
- Graph
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- Supertypes
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class Objecttrait Matchableclass Any
- Self type
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Approximation.type
Members list
Value members
Concrete methods
Method to determine if the approximation can be considered converged. We use the convolution of the probability density functions (PDFs) to determine if the probability of overlap exceeds the value p.
Method to determine if the approximation can be considered converged. We use the convolution of the probability density functions (PDFs) to determine if the probability of overlap exceeds the value p.
Value parameters
- confidence
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a probability between 0 and 1 -- 0 would always result in true; 1 will result in false unless x1 actually is x2.
- dfByDx
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the derivative function.
- f
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the function.
- x
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a Number which will be compared with zero.
Attributes
- Returns
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a Try[Boolean].
Method to evaluate function f at value x.
Method to evaluate function f at value x.
Value parameters
- dfByDx
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the derivative of the function.
- f
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the function.
- x
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the value to pass into f.
Attributes
- Returns
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the function's value at x.
Method to evaluate function f at value x. We ignore the derivative of the function at x. NOTE: this has consequences in terms of the precision of the result.
Method to evaluate function f at value x. We ignore the derivative of the function at x. NOTE: this has consequences in terms of the precision of the result.
Value parameters
- f
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the function.
- x
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the value to pass into f.
Attributes
- Returns
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the function's value at x.
Method used by solve to iterate towards a solution. This method of iterating towards a root of a continuously differentiable function implements Householder's method in general. The number of functions provided is the "order" of the method. The Newton-Raphson method is Householder's method, order 1. The Halley method is Householder's method, order 2. And so on.
Method used by solve to iterate towards a solution. This method of iterating towards a root of a continuously differentiable function implements Householder's method in general. The number of functions provided is the "order" of the method. The Newton-Raphson method is Householder's method, order 1. The Halley method is Householder's method, order 2. And so on.
Value parameters
- functions
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the derivatives of the function, starting with the 0th, i.e., the function itself.
Attributes
This method of finding a root of a continuously differentiable function implements Householder's method in general. The number of functions provided is the "order" of the method. The Newton-Raphson method is Householder's method, order 1. The Halley method is Householder's method, order 2. And so on. f[n](x) is the nth derivative of x, such that f[0](x) = f(x) and f[1](x) = f'(x) = d(f(x))/dx.
This method of finding a root of a continuously differentiable function implements Householder's method in general. The number of functions provided is the "order" of the method. The Newton-Raphson method is Householder's method, order 1. The Halley method is Householder's method, order 2. And so on. f[n](x) is the nth derivative of x, such that f[0](x) = f(x) and f[1](x) = f'(x) = d(f(x))/dx.
Value parameters
- confidence
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the confidence we need for the resulting root to be the same as zero.
- functions
- target
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the target value, by default, this will be a fuzzy version of (Double) zero.
- x0
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the initial guess.