Polynomial {assist} | R Documentation |

## Calculate Reproducing Kernels for Polynomial Splines on [0, 1]

### Description

Return a matrix evaluating reproducing kernels for polynomial splines at observed points.

### Usage

```
linear(s, t=s)
cubic(s, t=s)
quintic(s, t=s)
septic(s, t=s)
```

### Arguments

`s` |
a vector of values in [0, 1], at which the kernels are evaluated. |

`t` |
an optional vector in [0, 1]. Default is the same as s. |

### Details

The reproducing kernels implemented in these functions are based on Bernoulli functions with domain [0, 1].

### Value

a matrix with the numbers of row and column equal to the lengths of s and t respectively. The [i, j] element is the reproducing kernel of linear, cubic, quintic, or septic spline evaluated at (s[i], t[j]).

### Author(s)

Chunlei Ke chunlei_ke@yahoo.com and Yuedong Wang yuedong@ucsb.edu

### References

Wahba, G. (1990). Spline Models for Observational Data. SIAM, Vol. 59.

### See Also

`ssr`

, `linear2`

, `cubic2`

,
`quintic2`

, `septic2`

### Examples

```
## Not run:
x<-seq(0, 1, len=10)
cubic(x)
## End(Not run)
```

[Package

*assist*version 3.1.9 Index]