The context of my question is how to compute high order derivates on direct numerical simulation of turbulent channel flow. It is of particular interest for fluid dynamics and turbulence research. I want to find the coefficients of a B-spline curve given the value of the resulting function on a set of collocatioin points. Is there any way to do it without resorting to solve a linear system each time I need to find the coefficients.My specific case is to interpolate using a 7-th order B-spline scheme with knots given, but the values are set on 'Greville Abscisae'. The knots are given in this address:     http://turbulence.pha.jhu.edu/docs/channel/y-knots.txtAnd the collocation ponits in this:     http://turbulence.pha.jhu.edu/docs/channel/y.txtThough not necessary, you can query any example of such coefficients on this website, just inputing the collocation points on this website:http://turbulence.pha.jhu.edu/webquery/query.aspxThe quantity I am seeking to interpolate is the velocity field for the channel dataset. I have never worked with b-splines before, so I might be missing something, but I haven't found anywere a way to compute the coefficients from the collocation points, and this is bothering me. Solve a linear system for each line (in this case, a 512 x 506) would be bothersome, since I would need to do this for each vertical line on each snapshot of the simulation, and I would like to avoid this as much as possible, but I am not finding any other alternative. 
Find B-spline coefficients from values on collocation points
finite difference;interpolation;spectral method;b spline