Question

any one who has notes of numerical analysis plz.send me i have required ​

Answer 1

Answer:

Step-by-step explanation:

The main goal of numerical analysis is to develop efficient algorithms for computing

precise numerical values of mathematical quantities, including functions, integrals, solu-

tions of algebraic equations, solutions of differential equations (both ordinary and partial),

solutions of minimization problems, and so on. The objects of interest typically (but not

exclusively) arise in applications, which seek not only their qualitative properties, but also

quantitative numerical data. The goal of this course of lectures is to introduce some of the

most important and basic numerical algorithms that are used in practical computations.

Beyond merely learning the basic techniques, it is crucial that an informed practitioner

develop a thorough understanding of how the algorithms are constructed, why they work,

and what their limitations are.

In any applied numerical computation, there are four key sources of error:

(i) Inexactness of the mathematical model for the underlying physical phenomenon.

(ii) Errors in measurements of parameters entering the model.

(iii) Round-off errors in computer arithmetic.

(iv) Approximations used to solve the full mathematical system.

Of these, (i) is the domain of mathematical modeling, and will not concern us here. Neither

will (ii), which is the domain of the experimentalists. (iii) arises due to the finite numerical

precision imposed by the computer. (iv) is the true domain of numerical analysis, and

refers to the fact that most systems of equations are too complicated to solve explicitly, or,

even in cases when an analytic solution formula is known, directly obtaining the precise

numerical values may be difficult.

There are two principal ways of quantifying computational errors.

Definition 1.1. Let x be a real number and let x

⋆ be an approximation. The

absolute error in the approximation x

⋆ ≈ x is defined as | x

⋆ − x |. The relative error is

defined as the ratio of the absolute error to the size of x, i.e.,

| x

⋆ − x |

| x |

, which assumes

x 6= 0; otherwise relative error is not defined.