Recent questions tagged numerical-methods

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1

Which books are good to practice linear algebra and calculas?

asked Oct 1, 2018 in GATE by aditi19 Active (5.1k points) | 60 views

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1 answer

2

Syllabus:Numerical methods like newton method or bisection method part of syllabus of Gate?

asked Sep 15, 2018 in Mathematical Logic by bts1jimin (199 points) | 37 views

+2 votes

1 answer

3

#Numerical methods-syllabus
What is the syllabus for Engineering Mathematics - Numerical methods?

asked Oct 13, 2017 in Mathematical Logic by Swati Rauniyar Active (2.2k points) | 470 views

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1 answer

4

Virtual Gate Test Series: Numerical Ability - Percentage
A country’s GDP grew by $7.8%$ within a period. During the same period, the country’s per-capita-GDP (= ratio of GDP to the total population) increased by $10%.$ During this period, the total population of the country$?$ increased by $4\%$ decreased by $4\%$ increased by $2\%$ decreased by $2\%$

asked Jan 19, 2017 in Numerical Ability by Purple Active (3k points) | 214 views

+1 vote

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5

GATE1988-1i
Loosely speaking, we can say that a numerical method is unstable if errors introduced into the computation grow at _________ rate as the computation proceeds.

asked Dec 10, 2016 in Numerical Methods by jothee Veteran (105k points) | 114 views

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6

GATE1987-11b
Use Simpson's rule with $h=0.25$ to evaluate $ V= \int_{0}^{1} \frac{1}{1+x} dx$ correct to three decimal places.

asked Nov 15, 2016 in Numerical Methods by makhdoom ghaya Boss (30.2k points) | 216 views

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7

GATE1987-11a
Given $f(300)=2,4771; f(304) = 2.4829; f(305) = 2.4843$ and $f(307) = 2.4871$ find $f(301)$ using Lagrange's interpolation formula.

asked Nov 15, 2016 in Numerical Methods by makhdoom ghaya Boss (30.2k points) | 169 views

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8

GATE1987-1-xxv
Which of the following statements is true in respect of the convergence of the Newton-Rephson procedure? It converges always under all circumstances. It does not converge to a tool where the second differential coefficient changes sign. It does not converge to a root where the second differential coefficient vanishes. None of the above.

asked Nov 9, 2016 in Numerical Methods by makhdoom ghaya Boss (30.2k points) | 220 views

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9

GATE1987-1-xxiv
The simplex method is so named because It is simple. It is based on the theory of algebraic complexes. The simple pendulum works on this method. No one thought of a better name.

asked Nov 9, 2016 in Numerical Methods by makhdoom ghaya Boss (30.2k points) | 175 views

+3 votes

2 answers

10

ISRO2009-51
The formula $P_k = y_0 + k \triangledown y_0+ \frac{k(k+1)}{2} \triangledown ^2 y_0 + \dots + \frac{k \dots (k+n-1)}{n!} \triangledown ^n y_0$ is Newton's backward formula Gauss forward formula Gauss backward formula Stirling's formula

asked Jun 15, 2016 in Numerical Methods by jothee Veteran (105k points) | 1.1k views

+3 votes

1 answer

11

ISRO2009-47
The formula $\int\limits_{x0}^{xa} y(n) dx \simeq h/2 (y_0 + 2y_1 + \dots +2y_{n-1} + y_n) - h/12 (\triangledown y_n - \triangle y_0)$ $- h/24 (\triangledown ^2 y_n + \triangle ^2 y_0) -19h/720 (\triangledown ^3 y_n - \triangle ^3 y_0) \dots $ is called Simpson rule Trapezoidal rule Romberg's rule Gregory's formula

asked Jun 15, 2016 in Numerical Methods by jothee Veteran (105k points) | 987 views

+7 votes

1 answer

12

ISRO2009-44
A root $\alpha$ of equation $f(x)=0$ can be computed to any degree of accuracy if a 'good' initial approximation $x_0$ is chosen for which $f(x_0) > 0$ $f (x_0) f''(x_0) > 0$ $f(x_0) f'' (x_0) < 0$ $f''(x_0) >0$

asked Jun 3, 2016 in Numerical Methods by Desert_Warrior Loyal (7.9k points) | 1.7k views

+3 votes

2 answers

13

ISRO-2013-48
The Guass-Seidal iterative method can be used to solve which of the following sets? Linear algebraic equations Linear and non-linear algebraic equations Linear differential equations Linear and non-linear differential equations

asked Apr 29, 2016 in Numerical Methods by makhdoom ghaya Boss (30.2k points) | 1.5k views

+1 vote

2 answers

14

GATE2015 EC-1: GA-5
If $\log_{x}{(\frac{5}{7})}=\frac{-1}{3},$ then the value of $x$ is $343/125$ $25/343$ $-25/49$ $-49/25$

asked Feb 12, 2016 in Numerical Ability by Akash Kanase Boss (41.5k points) | 2k views

+11 votes

3 answers

15

GATE2015-3-50
The velocity $v$ (in kilometer/minute) of a motorbike which starts form rest, is given at fixed intervals of time $t$ (in minutes) as follows: t 2 4 6 8 10 12 14 16 18 20 v 10 18 25 29 32 20 11 5 2 0 The approximate distance (in kilometers) rounded to two places of decimals covered in 20 minutes using Simpson's $1/3^{rd}$ rule is ________.

asked Feb 16, 2015 in Numerical Methods by jothee Veteran (105k points) | 1.4k views

+7 votes

2 answers

16

GATE2015-2-39
The secant method is used to find the root of an equation $f(x)=0$. It is started from two distinct estimates $x_a$ and $x_b$ for the root. It is an iterative procedure involving linear interpolation to a root. The iteration stops if $f(x_b)$ is very small and then $x_b$ is the solution. ... $x_b - (x_b-x_a) f_b / (f_b-f(x_a)) $ $x_a - (x_b-x_a) f_a / (f_b-f(x_a)) $

asked Feb 13, 2015 in Numerical Methods by jothee Veteran (105k points) | 1.3k views

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1 answer

17

calculus
The estimate of $\int_{0.5}^{1.5}\frac{dx}{x}$ obtained using Simpson’s rule with threepoint function evaluation exceeds the exact value by (A) 0.235 (B) 0.068 (C) 0.024 (D) 0.012

asked Jan 30, 2015 in Numerical Methods by Nisha kumari (317 points) | 242 views

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18

2012 numerical methed

asked Jan 29, 2015 in Numerical Methods by Nisha kumari (317 points) | 110 views

+1 vote

1 answer

19

GATE2005-IT-2
If the trapezoidal method is used to evaluate the integral obtained $\int_{0}^{1} x^2dx$, then the value obtained is always > (1/3) is always < (1/3) is always = (1/3) may be greater or lesser than (1/3)

asked Nov 3, 2014 in Numerical Methods by Ishrat Jahan Boss (16.3k points) | 375 views

+2 votes

2 answers

20

GATE2004-IT-39
Consider the following iterative root finding methods and convergence properties: Iterative root finding methods Convergence properties Q. False Position I. Order of convergence = 1.62 R. Newton Raphson II. Order of convergence = 2 S. Secant III. Order of convergence = 1 with guarantee of convergence T. Successive ... , R-II, S-I, T-IV Q-II, R-I, S-IV, T-III Q-I, R-IV, S-II, T-III

asked Nov 2, 2014 in Numerical Methods by Ishrat Jahan Boss (16.3k points) | 259 views

+2 votes

1 answer

21

GATE2004-IT-38
If f(l) = 2, f(2) = 4 and f(4) = 16, what is the value of f(3) using Lagrange's interpolation formula? 8 8(1/3) 8(2/3) 9

asked Nov 2, 2014 in Numerical Methods by Ishrat Jahan Boss (16.3k points) | 313 views

0 votes

1 answer

22

GATE2006-IT-77
$x + y/2 = 9$ $3x + y = 10$ What can be said about the Gauss-Siedel iterative method for solving the above set of linear equations? it will converge It will diverse It will neither converge nor diverse It is not applicable

asked Nov 1, 2014 in Linear Algebra by Ishrat Jahan Boss (16.3k points) | 589 views

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1 answer

23

GATE2006-IT-76
x + y/2 = 9 3x + y = 10 The value of the Frobenius norm for the above system of equations is $0.5$ $0.75$ $1.5$ $2.0$

asked Nov 1, 2014 in Linear Algebra by Ishrat Jahan Boss (16.3k points) | 597 views

+6 votes

2 answers

24

GATE2006-IT-28
The following definite integral evaluates to $\int_{-\infty}^{0} e^ {-\left(\frac{x^2}{20} \right )}dx$ $\frac{1}{2}$ $\pi \sqrt{10}$ $\sqrt{10}$ $\pi$

asked Oct 31, 2014 in Numerical Methods by Ishrat Jahan Boss (16.3k points) | 1k views

0 votes

2 answers

25

GATE2006-IT-27
Match the following iterative methods for solving algebraic equations and their orders of convergence. Method Order of Convergence 1. Bisection P. 2 or more 2. Newton-Raphson Q. 1.62 3. Secant R. 1 4. Regula falsi S. 1 bit per iteration I-R, II-S, III-P, IV-Q I-S, II-R, III-Q, IV-P I-S, II-Q, III-R, IV-P I-S, II-P, III-Q, IV-R

asked Oct 31, 2014 in Numerical Methods by Ishrat Jahan Boss (16.3k points) | 255 views

+4 votes

1 answer

26

GATE2007-IT-77
Consider the sequence $\left \langle x_n \right \rangle,\; n \geq 0$ defined by the recurrence relation $x_{n + 1} = c \cdot (x_n)^2 - 2$, where $c > 0$. For which of the following values of $c$, does there exist a non-empty open interval $(a, b)$ such that the sequence $x_n$ ... $0.25$ $0.35$ $0.45$ $0.5$ i only i and ii only i, ii and iii only i, ii, iii and iv

asked Oct 31, 2014 in Numerical Methods by Ishrat Jahan Boss (16.3k points) | 576 views

0 votes

1 answer

27

GATE2007-IT-22
The trapezoidal method is used to evaluate the numerical value of $\int_{0}^{1}e^x dx$. Consider the following values for the step size h. 10-2 10-3 10-4 10-5 For which of these values of the step size h, is the computed value guaranteed to be correct to ... Assume that there are no round-off errors in the computation. iv only iii and iv only ii, iii and iv only i, ii, iii and iv

asked Oct 30, 2014 in Numerical Methods by Ishrat Jahan Boss (16.3k points) | 434 views

0 votes

1 answer

28

GATE2008-IT-30
Consider the function f(x) = x2 - 2x - 1. Suppose an execution of the Newton-Raphson method to find a zero of f(x) starts with an approximation x0 = 2 of x. What is the value of x2, the approximation of x that algorithm produces after two iterations, rounded to three decimal places? 2.417 2.419 2.423 2.425

asked Oct 28, 2014 in IS&Software Engineering by Ishrat Jahan Boss (16.3k points) | 247 views

+4 votes

2 answers

29

GATE1996-2.5
Newton-Raphson iteration formula for finding $\sqrt[3]{c}$, where $c > 0$ is $x_{n+1}=\frac{2x_n^3 + \sqrt[3]{c}}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 - \sqrt[3]{c}}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 + c}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 - c}{3x_n^2}$

asked Oct 9, 2014 in Numerical Methods by Kathleen Veteran (52.2k points) | 412 views

0 votes

3 answers

30

GATE1995-2.15
The iteration formula to find the square root of a positive real number $b$ using the Newton Raphson method is $x_{k+1} = 3(x_k+b)/2x_k$ $x_{k+1} = (x_{k}^2+b)/2x_k$ $x_{k+1} = x_k-2x_k/\left(x^2_k+b\right)$ None of the above

asked Oct 8, 2014 in Numerical Methods by Kathleen Veteran (52.2k points) | 528 views

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