mpoly (version 1.1.1)

bernstein-approx: Bernstein polynomial approximation

Description

Bernstein polynomial approximation

Usage

bernstein_approx(f, n, lower = 0, upper = 1, indeterminate = "x")
bernsteinApprox(...)

Arguments

f

the function to approximate

n

Bernstein polynomial degree

lower

lower bound for approximation

upper

upper bound for approximation

indeterminate

indeterminate

...

...

Value

a mpoly object

Examples

# NOT RUN {




# }
# NOT RUN {
  # visualize the bernstein polynomials

library(ggplot2); theme_set(theme_bw())
library(reshape2)




f <- function(x) sin(2*pi*x)
p <- bernstein_approx(f, 20)
round(p, 3)

x <- seq(0, 1, length.out = 101)
df <- data.frame(
  x = rep(x, 2),
  y = c(f(x), as.function(p)(x)),
  which = rep(c("actual", "approx"), each = 101)
)
qplot(x, y, data = df, geom = "line", color = which)






p <- bernstein_approx(sin, 20, pi/2, 1.5*pi)
round(p, 4)

x <- seq(0, 2*pi, length.out = 101)
df <- data.frame(
  x = rep(x, 2),
  y = c(sin(x), as.function(p)(x)),
  which = rep(c("actual", "approx"), each = 101)
)
qplot(x, y, data = df, geom = "line", color = which)








p <- bernstein_approx(dnorm, 15, -1.25, 1.25)
round(p, 4)

x <- seq(-3, 3, length.out = 101)
df <- data.frame(
  x = rep(x, 2),
  y = c(dnorm(x), as.function(p)(x)),
  which = rep(c("actual", "approx"), each = 101)
)
qplot(x, y, data = df, geom = "line", color = which)






# }
# NOT RUN {
# }