Question

3. (a) Define the Jacobian matrix, J, of a set of algebraic equations fx). 151 (b) It is not always possible to obtain the analytical or symbolic expressions in the Jacobian matrix. Suggest some other ways of obtaining the Jacobian matrix in such cases 151 (c) Carry out one iteration of Newton's method for the following problem starting from the point x -[1 1] 101 f2 =x(+4x2 +5-0 (d) What is the role of Gaussian Elimination in Newton's method? 15] CONTINUED

Answer 1

AS: (9) Jaco bian Matrix-The Jacobian ιδ # dalives. You uFor example s tthe matai is eqwation is tobich has paotial dleivadives, dT dA す万-0 下 This aives us the ool Tacobian 0 BT iKewise compute paxal olavivatives othor equations Pusm Set and we can obtain tho Haco bian madxala se olglboic equadtien

(b) I dont Knou ang othex coay bu you use MATLAB SoHwaðe to lind analytical or olic expoeseions n Jacobian mat oix. (d) Meuotonls me-hod says : Thi ai r one- dimengional fbomela , uohi ch ge by goving tho equation an u implementod, iS in -ths mielfvcsriable case , zn is a Bequence lvectos, obtained by fi an intialguess zo and than golving the System- This is why you need ausmiar elimination, intad of manualy6olving. as in the one-dimensiu ease, we are tin a computer 9ovve fr ug
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