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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