• a Lagrange approach (use divided differences)
• a Hermite approach (use divided differences)
• a piecewise cubic Hermite approach
• a cubic spline approach

Some algorithms you might find useful:

• Click Here for an algorithm which performs Horner's Evaluation of Polynomials
• Click Here for an algorithm which creates and solves using the matrix approach
• Click Here for an algorithm which plots the Lagrange polynomial using the matrix approach.
• Click Here for the m-file which computes the Newton's Divided Differences
• Click Here for the m-file which computes the Lagrange polynomial using Horner's approach.
• Click Here for the m-file which computes the Hermite Divided Differences.
• Click Here for the m-file which computes the Hermite polynomial using Horner's approach.
• Click Here for an m-file which computes Cubic Splines
• You'll also need this one to get the coefficients
• You'll also need this tri-diagonal system solver to get the coefficients