Download presentation

Presentation is loading. Please wait.

Published byNatasha Beddingfield Modified over 2 years ago

1
Polynomial Evaluation

2
Straightforward Evaluation P(x) = 3x 5 +2x 4 +7x 3 +8x 2 +2x+4P(x) = 3x 5 +2x 4 +7x 3 +8x 2 +2x+4 t1 = (3*x*x*x*x*x)t1 = (3*x*x*x*x*x) t2 = t1 + (2*x*x*x*x)t2 = t1 + (2*x*x*x*x) t3 = t2 + (7*x*x*x)t3 = t2 + (7*x*x*x) t4 = t3 + (8*x*x)t4 = t3 + (8*x*x) P = t4 +(2*x) + 4P = t4 +(2*x) + 4 15 Multiplications, 5 Additions15 Multiplications, 5 Additions

3
A Little Smarter P(x) = 3x 5 +2x 4 +7x 3 +8x 2 +2x+4P(x) = 3x 5 +2x 4 +7x 3 +8x 2 +2x+4 t1 := 4; xp := x;t1 := 4; xp := x; t2 := (2*xp) + t1; xp := xp * x;t2 := (2*xp) + t1; xp := xp * x; t3 := (8*xp) + t2; xp := xp * x;t3 := (8*xp) + t2; xp := xp * x; t4 := (7*xp) + t3; xp := xp * x;t4 := (7*xp) + t3; xp := xp * x; t5 := (2*xp) + t4; xp := xp * x;t5 := (2*xp) + t4; xp := xp * x; P := (3*xp) + t5;P := (3*xp) + t5; 9 Multiplications, 5 Additions9 Multiplications, 5 Additions

4
Horner’s Rule P(x) = 3x 5 +2x 4 +7x 3 +8x 2 +2x+4P(x) = 3x 5 +2x 4 +7x 3 +8x 2 +2x+4 t1 = (3*x) + 2t1 = (3*x) + 2 t2 = (t1*x) + 7t2 = (t1*x) + 7 t3 = (t2*x) + 8t3 = (t2*x) + 8 t4 = (t3*x) + 2t4 = (t3*x) + 2 P = (t4*x) + 4P = (t4*x) + 4 5 Multiplications, 5 Additions5 Multiplications, 5 Additions

5
Computing Powers xp := x; pwork := power; Res := 1; While pwork > 0 Do If pwork mod 2 = 1 then If pwork mod 2 = 1 then Res := Res * xp; Res := Res * xp; End If End If xp := xp * xp; xp := xp * xp; pwork := pwork / 2; /* integer division */ pwork := pwork / 2; /* integer division */ End While

6
For Power = 15 6 Multiplications by Squaring Algorithm6 Multiplications by Squaring Algorithm An Alternative Procedure:An Alternative Procedure: p = x * xp = x * x p = p * p *xp = p * p *x p = p * p * pp = p * p * p 5 Multiplications by Factorization5 Multiplications by Factorization

Similar presentations

OK

10.6 – Special Products of Polynomials Multiplying Two Binomials using FOIL First termsLast termsInner termsOuter terms.

10.6 – Special Products of Polynomials Multiplying Two Binomials using FOIL First termsLast termsInner termsOuter terms.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on different types of plants Ppt on endangered and extinct animals Ppt on accounts payable process Ppt on popular social networking sites Ppt on economic systems Ppt on motivational stories Topics for ppt on environmental pollution By appt only Download ppt on wildlife conservation in india Ppt on interest rate swaps