Interpolation Methods

Interpolation is the way to estimating a function at intermediate point. There are some methods of interpolation as I refer to Wikipedia:

1. Piecewise constant interpolation : locate the nearest data value and assign the same value.

Piecewise constant interpolation

2. Linear interpolation : taking the midway value between two data points into the a linear function.

Linear interpolation superimposed

3. Polynomial interpolation : is a generalization of linear interpolation by replacing interpolant with a polynomial of higher degree.

Polynomial interpolation plot

4. Spline interpolation : is an interpolation using low-degree polynomial in each intervals and chooses the polynomial pieces such that they fit smoothly together.

Spline intepolation plot

Well-posed vs. Ill-posed problems

Biar tidak lupa, berikut adalah catatan super singkat tentang definisi Well-posed problem dan ill-posed problem.

Jadi, menurut wikipedia, well-posed problem adalah model matematika untuk fenomena fisika yang memenuhi syarat :

1. Ada jawaban pasti dari model matematika tersebut
2. Jawaban atau solusi dari model matematika tersebut unik
3. Sifat jawaban atau solusi dari model matematika tersebut berubah sesuai kondisi awal (soalnya)

Sebaliknya, model matematika yang tidak memenuhi ketiga syarat tersebut disebut ill-posed problem, misalnya inverse problem, and continuum model.