Lecture 4 Printed Notes

Lecture 4 Printed Notes - equations using matrices. i)...

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ME 218: ENGR COMPUTATIONAL METHODS Lecture Notes (Set #4) Secant Method To overcome the need in the Newton-Raphson iterative scheme to evaluate first derivative of the function, or the possibility of the derivative going to zero, the Secant Method can be used. It utilizes the information of a second point to evaluate the derivative, by assuming that the function is linear in the domain of interest. From the Newton-Raphson’s method: x 2 = x 0 – f(x 0 )/f’(x 0 ) But using another point, x 1 , between x 2 and x 0 to determine the derivative, f’(x 0 ) : f’(x 0 ) = (f(x 1 ) – f(x 0 ))/(x 1 – x 0 ) Thus, generalizing the iterative scheme: The computation of the derivative is avoided by using two starting values, x 0 and x 1 ! Matrix Algebra A matrix is a rectangular array of numbers in which not only the value of the number is important, but also its position in the array. It is very easy to solve a system of linear
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Unformatted text preview: equations using matrices. i) Matrix Addition Two matrices of the same size may be added or subtracted. Then, A+C is not defined since A is a and C is a matrix! ii) Matrix Multiplication If A and B are two given matrices, then the product AB is only defined if the number of columns of A is equal to the number of rows of B , and the product matrix has the number of rows of A and the number of columns of B . For this reason, AB may not be equal to BA ! Example is not defined. A is a matrix and C is a matrix. The number of columns of A the number of rows of C . iii) Transpose of a Matrix If the rows of a given matrix are interchanged with the columns of the same matrix, the resultant matrix is the transpose of the given matrix....
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Lecture 4 Printed Notes - equations using matrices. i)...

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