Copyright (c) Edward Kmett 2015 BSD3 ekmett@gmail.com experimental GHC only None Haskell2010

Contents

Description

Synopsis

# Newton's Method (Forward)

findZero :: (ForwardDouble -> ForwardDouble) -> Double -> [Double] Source

The `findZero` function finds a zero of a scalar function using Newton's method; its output is a stream of increasingly accurate results. (Modulo the usual caveats.) If the stream becomes constant ("it converges"), no further elements are returned.

Examples:

````>>> ````take 10 \$ findZero (\x->x^2-4) 1
```[1.0,2.5,2.05,2.000609756097561,2.0000000929222947,2.000000000000002,2.0]
```

inverse :: (ForwardDouble -> ForwardDouble) -> Double -> Double -> [Double] Source

The `inverse` function inverts a scalar function using Newton's method; its output is a stream of increasingly accurate results. (Modulo the usual caveats.) If the stream becomes constant ("it converges"), no further elements are returned.

Example:

````>>> ````last \$ take 10 \$ inverse sqrt 1 (sqrt 10)
```10.0
```

fixedPoint :: (ForwardDouble -> ForwardDouble) -> Double -> [Double] Source

The `fixedPoint` function find a fixedpoint of a scalar function using Newton's method; its output is a stream of increasingly accurate results. (Modulo the usual caveats.)

If the stream becomes constant ("it converges"), no further elements are returned.

````>>> ````last \$ take 10 \$ fixedPoint cos 1
```0.7390851332151607
```

extremum :: (On (Forward ForwardDouble) -> On (Forward ForwardDouble)) -> Double -> [Double] Source

The `extremum` function finds an extremum of a scalar function using Newton's method; produces a stream of increasingly accurate results. (Modulo the usual caveats.) If the stream becomes constant ("it converges"), no further elements are returned.

````>>> ````last \$ take 10 \$ extremum cos 1
```0.0
```