MATLAB FINANCIAL DERIVATIVES TOOLBOX Manual de usuario descargar pdf (Pagina 50)

bxa...xaxa

=+++

2211

221222121

11212111

The solution of the above system can be expressed as:

bAx

1−

given that “

1−

” (that represents the inverse matrix of “

”) exists and the

number of equation, n, is equal or greater than the number of unknowns, m.

A unique solution to the above equation system exists when: n=m.

Matlab has standard and efficient specialized routines to solve such systems

like the

e function (called alternatively with “\”). Otherwise, a quick

way (but some times non practical and inaccurate if the number of

equations is extremely large) to solve the above system is via the inverse

function,

v (note that the

v can be used only with square matrices). View

the following example to understand how you can solve a small system of

linear equations:

Matlab’s command:

>> clear; A=[2 4 3; -2 -4 2; 6 4 2]; b=[2 ;4;1];

>> x1=inv(A)*b, x2=A\b

Matlab’s response:

x1 =

0.0500

-0.4250

1.2000

x2 =

0.0500

-0.4250

1.2000

Comments:

Two ways for solving a system of linear equations.

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MATLAB FINANCIAL DERIVATIVES TOOLBOX Manual de usuario Pagina 50