P

Please be clear and include all steps, thank you!

EXTRA PROBLEM (4 pts.): Let Printerpolate f at n+1 distinct points. Consider Prin its Lagrange and Newton forms j-1 Dr() a; IT (1-1) k=1.k#j :1-2) j=0 with a; = (x;) ; 1/(tj - Da) and c; = /[:30, ..., ]. Suppose that we will evaluate Pr many times for different values of r. Thus, we can precompute the values of a, and c; and then can use them without any cost. For both forms, propose efficient in terms of arithmetic operations) algorithms for computing (2). Which form admits less expensive algorithm? EXTRA PROBLEM (4 pts.): Let Printerpolate f at n+1 distinct points. Consider Prin its Lagrange and Newton forms j-1 Dr() a; IT (1-1) k=1.k#j :1-2) j=0 with a; = (x;) ; 1/(tj - Da) and c; = /[:30, ..., ]. Suppose that we will evaluate Pr many times for different values of r. Thus, we can precompute the values of a, and c; and then can use them without any cost. For both forms, propose efficient in terms of arithmetic operations) algorithms for computing (2). Which form admits less expensive algorithm