# Numerical Computation Class 11 Mathematics Solutions | Exercise - 19.2

## Chapter - 19

__Numerical Computation__

Numerical Computation is a compulsory chapter in class 11 mathematics, which means you can't skip this chapter. I personally don't understand this chapter completely; it's a confusing type of chapter that I don't like.

Like me you guys were also facing problem while solveing the question guven in exercise. Some of you were even demanding the notes of class 11 Numerical Computation chapter. We were continuously getting text through our social media handles. So, I'm here to fulfill your wish. Today I'll be giving you the complete note of class 11 Numerical Computation chapter. For further information keep on reading this article.

We already have discussed a lot about Numerical Computation in our previous article. I'm talking about the article where I have provided you the complete notes of exercise 19.1. In that article I discussed about characteristics of numerical computations. I only listed the names of the characteristics.

So let's learn in brief about those characteristics for getting a better understanding of this chapter. If you haven't read the previous article then make sure to read it before reading this one.

**Characteristics of Numerical Computing**

- Accuracy
- Rate of convergence
- Numerical stability, and
- Efficiency

#### Accuracy

Accuracy refers to how well a method matches the expected result. It can also be interpreted as the degree to which a given quantity is correct and free from error. For example, quantity specified as 100±1 has an (absolute) accuracy of ±1 (meaning its true value can fall in the range 99-101), while a quantity specified as 100-+2 has an accuracy of ±2 meaning its true value can fall in the range 98-102.

#### Rate of convergence

Rate of convergence refers to how long it takes to apply a given method for a given time- step. Suppose that the sequence {xₖ} of values converges to a number L.

#### Numerical stability

Numerical stability refers to how well the method copes with stiff constraints before error becomes unacceptable large. Numerical stability is considered to be a desirable property of numerical algorithms.

Its precise definition depends on the context and is related to the accuracy of the algorithms. Depending on the specific computational method small errors, instead of damped, can be magnified leading to large errors

#### Efficiency

Efficiency refers to the number of steps in the algorithm, the computer time, and the amount of the computer (or computing device) that is required.

### Exercise - 19.2

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