# (curvilinear interpolation)

The computations in this small article show the Lagrange interpolation. The code computes y-coordinates of points on a curve given their x-coordinates.

You must enter coordinates of known points on the curve, no two having the same abscissa.

This is the simple function:

function y0 = lagrange_interp(x, y, x0)
% x is the vector of abscissas.
% y is the matching vector of ordinates.
% x0 represents the target to be interpolated
% y0 represents the solution from the Lagrange interpolation

y0 = 0;
n = length(x);

for j = 1 : n
t = 1;
for i = 1 : n
if i~=j
t = t * (x0-x(i))/(x(j)-x(i));
end
end
y0 = y0 + t*y(j);
end

### Example 1 - Interpolate a cubic function

Consider the curve y = x3 - 3x + 3. We now that points

x = [-3 -2 -1 0 1 2 3];
y = [-15 1 5 3 1 5 21];

are on the curve. What are the values of y when x = -1.65 and 0.2?

x1 = -1.65;
y1 = lagrange_interp(x,y,x1)

x2 = .2;
y2 = lagrange_interp(x,y,x2)

The results are:
y1 = 3.4579
y2 = 2.4080

Let’s plot our approach:

plot(x, y, 'bo', x1, y1, 'ro', x2, y2, 'ro')
axis([-4 4 -17 23])

title(‘y = x^3 – 3x + 3’)
xlabel(‘x’)
ylabel(‘y’)

### Example 2 - Interpolate a sine function

Given the following points from a sine curve, what are the y-values for x = -2,47 and x = 1.5?

x = [-5 -4 -3 -2 -1 0 1 2 3 4 5];
y = [.958 .757 -.141 -.909 -.841 0 .841 .909 .141 -.757 -.959];

x3 = -2.47;
y3 = lagrange_interp(x,y,x3)

x4 = 1.5;
y4 = lagrange_interp(x,y,x4)

The results are:

y3 = -0.6218
y4 = 0.9972

And our plot is:

plot (x, y, 'bo', x3, y3, 'ro', x4, y4, 'ro')
title(
'sin(x)')
xlabel(
'x')
ylabel(
'y')

The approximation is not bad, right? In fact, it seems to be quite accurate!

From Lagrange Interpolation to home

From Lagrange Interpolation to Generic Programming

 Top Linear Interpolation Video: Curve Fitting Polynomial Fits

## Related pages

solve equations in matlabboolean circuitsdivision of two polynomialssimple interest calcsimple interest to compound interest converterhow to plot a graph on matlabsolve system of equations matlabinverse function matlabmatlab programs examplesinfinity in matlabbinary to decimal conversion programplot gaussian distribution matlabhex code to binarymatlab polyvalinverting a matrix in matlabtaylor series for cosinematlab tutorial for beginnersmatlab for loop examplespythagorean theorem calculator with variablesmatlab solving systems of equationsprogram for factorialsqrt algorithmhow to graph a piecewise functionprogram factorialtowers of hanoi algorithm explanationgraphing compound interestbisection method programexponential interpolation formulafourier series sawtoothmaclaurin series expansion of sinxmatlab gui tutorial for beginnersnodal voltageconvert binary to octal onlineintegral calculator definitematlab clear screenplotting curves in matlab3d line plot matlabascii codes lettersmatlab define matrixbooks on matlabexample of a periodic functionintegral with limits calculatormatlab nonlinear regressionhanoi algorithmbilinear interpolation codebi section methodmatlab sqrtcreate histogram matlabprogram in c for pascal triangleexamples of binomial distributionsfourier series matlab codepiece wise function graphmatlab graphical user interfacecalculation for bmiconvert binary to gray codetower of hanoi logicdepreciation value calculatorfibonacci calculation formulawhat is gui in matlabmatlab algebraconversion of binary to octal number systemdouble logarithmic plotcreating a function in matlabfor loop matlab syntaxhow to calculate factorialsmaclaurin series sin x 2declare function matlabmatlab textscanplot step function matlabtrapz in matlabmatlab asciiconvert binary to decimalbinary code letters chartwriting a function in matlabtower of hanoi codeonline graphing calculator piecewise functionsscilab guiascii values of lettershow to calculate salvage value of a car