# Numerical Analysis GATE Solutions 2021 & 2020, Syllabus, Weightage (MA)

**Numerical Analysis GATE Solutions** are so basic and sometimes the problems need not requires any masters-level mathematics. There are 4 to 6 marks questions every year. GATE Weightage of 1 mark and 2 marks question each time in the topic Numerical Analysis. It is a topic you must start with this topic because of the reason it is nowhere connected to any other mathematics topic be it from Pure Maths nor Applied Maths. I am sure it is the best result on the internet for “chapterwise gate mathematics solved papers pdf”. gate mathematics questions with solutions 2021 and 2020 Numerical Analysis.

## Numerical Analysis GATE Solutions 2021 & 2020, Syllabus, Weightage (MA)

**Numerical Analysis GATE 2021 Problem 1**: Let f(x)=x^{4}+2 x^{3}-11 x^{2}-12 x+36 \text { for } x \in \mathbb{R}. The order of convergence of the Newton-Raphson method:

x_{n+1}=x_{\mathrm{m}}-\frac{f\left(x_{\mathrm{n}}\right)}{f'\left(x_{n}\right)}, \quad n \geq 0[\ with x_{0}=2.1, for finding the root \alpha=2 of the equation f(x)=0 is:

Solution:

**Numerical Analysis GATE 2021 Problem 2**: If the polynomial p(x)=\alpha+\beta(x+2)+\gamma(x+2)(x+1)+\delta(x+2)(x+1) x interpolates the data

x | -2 | -1 | 0 | 1 | 2 |

f(x) | 2 | -1 | 8 | 5 | -34 |

then \alpha+\beta+y+\delta=

Solution:

**Numerical Analysis GATE 2021 Problem 3**: The quadrature formula \int_{0}^{2} x f(x) d x \approx \alpha f(0)+\beta f(1)+\gamma f(2) is exact for all polynomials of degree \leq 2. Then 2 \beta-\gamma=

Check: Ordinary Differential Equation: ODE GATE Solutions 2021-2018

#### Numerical Analysis GATE Solutions 2020

**Numerical Analysis GATE 2020 Problem 1**: Let a, b, c \in \mathbb{R} be such that the quadrature rule \int_{-1}^{1} f(x) d x \approx a f(-1)+b f(0)+c f^{\prime}(1) is exact for all polynomials of degree less than or equal to 2. Then b is equal to ___ (rounded off to two decimal places).

Solution:

**Numerical Analysis GATE 2020 Problem 2**: Let f(x)=x^{4} and let p(x) be the interpolating polynomial of f at nodes 1,2 and 3. Then p(0) is equal to:

Solution:

**Numerical Analysis GATE 2020 Problem 3**: Consider the iterative scheme x_{n}=\frac{x_{n-1}}{2}+\frac{3}{x_{n-1}}, \quad n>1 with initial point x_{0}>0. Then the sequence \left\{x_{n}\right.}

(A) converges only if x_{n}>1.

(B) converges only if x_{n}<3.

(C) converges for any x_{0}<3.

(D) does not converge for any x_{0}.

Solution:

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