Class17 - Class meeting #17 Wednesday, Oct. 20th GEEN 1300...

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1 Class meeting #17 Wednesday, Oct. 20 th GEEN 1300 Introduction to Engineering Computing Excel & Visual Basic for Applications (VBA) designing the Gaussian Elimination algorithm implementation in VBA 1 Homework #8 posted, due Wednesday, November 10 th [double-weighted project assignment] Start by representing the set of equations in a general form: ax ax ax ax b b n nn 11 1 12 2 13 3 1n 1 21 1 22 2 23 3 2 2   ... a x b ax a x b ii i i i i in n i ki i k ii k n n k 11    , , 2 x b ni i ni i nn n n ,
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2 Abstract the coefficients and constants into an A matrix and b vector 11 12 13 1n 1 21 22 23 2n 2 aaa ab  ii i,i 1 in i ki k i 1 kn k aa a b a b  Current pivot element 3 k , i1 k n ni n,i 1 nn n a b Element below pivot in row k that is being reduced the “big picture” Gaussian Elimination Algorithm Design start do forward pass do back- substitution pass 4 end
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3 proceed from from row 1 to row n down through the augmented matrix start i=1 i=i+1 i>n ? end of forward T F normalize the i th row first reduce each now, expand this block normalize row i k=i+1 k=k+1 k>n ? pass T F 5 element below the i,i pivot all the way to the bottom reduce row k below pivot row i the j index goes across row i from column i+1 (one to the right of the pivot) to the end Normalize row i Note: we don’t have to divide a ii by itself to get 1. We already know that this will be the result, and we never use a ii again in the algorithm. j=i+1 j=j+1 j>n ? T F a ij = a ij / a ii b i = b i / a ii 6 divide the row element by the pivot element finally, divide the constant in row i by the pivot element
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4 proceed from from row 1 to row n down through the augmented matrix start i=1 i=i+1 i>n ?
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Class17 - Class meeting #17 Wednesday, Oct. 20th GEEN 1300...

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