need help in coding

29 Jun need help in coding

1. Matlab. Complete the quadratic equation solver yournameQuadEqn.m. See the comments at the top for specific directions, but the main idea is to avoid loss of significance by re-writing one of roots

 .

· The formula for the root r1 has potential loss of significance when b > 0 and b2 > 4ac; The second root r2 is best left as is.

· The formula for the root r2 has potential loss of significance when b < 0 and b2 > 4ac. The first r1 is best left as is.

2. Write a C program for estimating adding numbers in a 2D grid. See the file yournameGridSum.c to get started. This program will exhibit the effect of cumulative rounding error (caused by adding a lot small values.) Consider an N × N grid (we’ll use N = 5000) dividing up the unit square into smaller squares. Therefore each subsquare has width w = 1/N. Let (xi,yj) denote the midpoint of the square in column i, row j. Note that

xi = (i − 0.5) ∗ w

Your job is to compute the double sum

N N

S = 3w2XX(xi)2 + (yj)2

j=1 i=1

For N large, the value of S should approach 2. You will compute S in two different ways: I. Summing up the numbers 1 by 1 in a nested for loop.

PSEUDOCODE

Initialize: width=1/N; sum1=0;

for loop: row=1 to N for loop: col=1 to N x = (col -0.5)*width y = (row – 0.5)*width sum1 = sum1 + (x*x + y*y)

end of inner loop

end of outer loop finalResult1= 3*width*width*sum1

II. Sum all the number in a row, then add to overall sum.

PSEUDOCODE

Initialize: sum2=0;

for loop: row=1 to N

rowSum=0; y= (row – 0.5)*width for loop: col=1 to N x = (col -0.5)*width rowSum = rowSum + (x*x + y*y)

end of inner loop sum2=sum2+ rowSum

end of outer loop finalResult2= 3*width*width*sum2