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Recent questions tagged numericalmethods
Numerical Methods:
LU decomposition for systems of linear equations
Numerical solutions of nonlinear algebraic equations by Secant, Bisection and NewtonRaphson Methods
Numerical integration by trapezoidal and Simpson’s rules
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Which books are good to practice linear algebra and calculas?
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Oct 1, 2018
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linearalgebra
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Syllabus:Numerical methods like newton method or bisection method part of syllabus of Gate?
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Sep 15, 2018
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#Numerical methodssyllabus
What is the syllabus for Engineering Mathematics  Numerical methods?
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Oct 13, 2017
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Mathematical Logic
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numericalmethods
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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 percapitaGDP (= 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 $2\%$
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Jan 19, 2017
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Numerical Ability
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generalaptitude
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5
GATE19881i
Loosely speaking, we can say that a numerical method is unstable if errors introduced into the computation grow at _________ rate as the computation proceeds.
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Dec 10, 2016
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Numerical Methods
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jothee
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gate1988
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numericalmethods
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GATE198711b
Use Simpson's rule with $h=0.25$ to evaluate $ V= \int_{0}^{1} \frac{1}{1+x} dx$ correct to three decimal places.
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Nov 15, 2016
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Numerical Methods
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makhdoom ghaya
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gate1987
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numericalmethods
simpsonsrule
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GATE198711a
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.
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Nov 15, 2016
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Numerical Methods
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makhdoom ghaya
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gate1987
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numericalmethods
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GATE19871xxv
Which of the following statements is true in respect of the convergence of the NewtonRephson 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.
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Nov 9, 2016
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Numerical Methods
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makhdoom ghaya
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gate1987
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newtonraphson
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GATE19871xxiv
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.
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Nov 9, 2016
in
Numerical Methods
by
makhdoom ghaya
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gate1987
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simplexmethod
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+3
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2
answers
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ISRO200951
The formula $P_k = y_0 + k \triangledown y_0+ \frac{k(k+1)}{2} \triangledown ^2 y_0 + \dots + \frac{k \dots (k+n1)}{n!} \triangledown ^n y_0$ is Newton's backward formula Gauss forward formula Gauss backward formula Stirling's formula
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Jun 15, 2016
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Numerical Methods
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isro2009
numericalmethods
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ISRO200947
The formula $\int\limits_{x0}^{xa} y(n) dx \simeq h/2 (y_0 + 2y_1 + \dots +2y_{n1} + y_n)  h/12 (\triangledown y_n  \triangle y_0)$ $ 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
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Jun 15, 2016
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Numerical Methods
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isro2009
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12
ISRO200944
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 $f(x_0) > 0$ $f (x_0) f''(x_0) > 0$ $f(x_0) f'' (x_0) < 0$ $f''(x_0) >0$
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Jun 3, 2016
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Numerical Methods
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isro2009
numericalmethods
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ISRO201348
The GuassSeidal iterative method can be used to solve which of the following sets? Linear algebraic equations Linear and nonlinear algebraic equations Linear differential equations Linear and nonlinear differential equations
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Apr 29, 2016
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Numerical Methods
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makhdoom ghaya
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isro2013
numericalmethods
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GATE2015 EC1: GA5
If $\log_{x}{(\frac{5}{7})}=\frac{1}{3},$ then the value of $x$ is $343/125$ $25/343$ $25/49$ $49/25$
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Feb 12, 2016
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Numerical Ability
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Akash Kanase
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gate2015ec1
generalaptitude
numericalmethods
logarithms
+11
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GATE2015350
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 ________.
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Feb 16, 2015
in
Numerical Methods
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jothee
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gate20153
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numericalanswers
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2
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GATE2015239
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_bx_a) f_b / (f_bf(x_a)) $ $x_a  (x_bx_a) f_a / (f_bf(x_a)) $
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Feb 13, 2015
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Numerical Methods
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jothee
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gate20152
numericalmethods
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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
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Jan 30, 2015
in
Numerical Methods
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Nisha kumari
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317
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242
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2012 numerical methed
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Jan 29, 2015
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Numerical Methods
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Nisha kumari
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317
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110
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outofsyllabusnow
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+1
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1
answer
19
GATE2005IT2
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)
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Nov 3, 2014
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Numerical Methods
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gate2005it
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trapezoidalrule
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2
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GATE2004IT39
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 ... , RII, SI, TIV QII, RI, SIV, TIII QI, RIV, SII, TIII
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Nov 2, 2014
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Numerical Methods
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Ishrat Jahan
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gate2004it
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1
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GATE2004IT38
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
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Nov 2, 2014
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Numerical Methods
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Ishrat Jahan
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gate2004it
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GATE2006IT77
$x + y/2 = 9$ $3x + y = 10$ What can be said about the GaussSiedel 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
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Nov 1, 2014
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Linear Algebra
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Ishrat Jahan
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gate2006it
linearalgebra
normal
numericalmethods
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GATE2006IT76
x + y/2 = 9 3x + y = 10 The value of the Frobenius norm for the above system of equations is $0.5$ $0.75$ $1.5$ $2.0$
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Nov 1, 2014
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Linear Algebra
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Ishrat Jahan
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gate2006it
linearalgebra
normal
numericalmethods
nongate
+6
votes
2
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GATE2006IT28
The following definite integral evaluates to $\int_{\infty}^{0} e^ {\left(\frac{x^2}{20} \right )}dx$ $\frac{1}{2}$ $\pi \sqrt{10}$ $\sqrt{10}$ $\pi$
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Oct 31, 2014
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Numerical Methods
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Ishrat Jahan
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gate2006it
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nongate
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GATE2006IT27
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. NewtonRaphson Q. 1.62 3. Secant R. 1 4. Regula falsi S. 1 bit per iteration IR, IIS, IIIP, IVQ IS, IIR, IIIQ, IVP IS, IIQ, IIIR, IVP IS, IIP, IIIQ, IVR
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Oct 31, 2014
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Numerical Methods
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Ishrat Jahan
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gate2006it
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+4
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1
answer
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GATE2007IT77
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 nonempty 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
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Oct 31, 2014
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Numerical Methods
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Ishrat Jahan
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gate2007it
numericalmethods
normal
nongate
0
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GATE2007IT22
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. 102 103 104 105 For which of these values of the step size h, is the computed value guaranteed to be correct to ... Assume that there are no roundoff errors in the computation. iv only iii and iv only ii, iii and iv only i, ii, iii and iv
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Oct 30, 2014
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Numerical Methods
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Ishrat Jahan
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gate2007it
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trapezoidalrule
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outofsyllabusnow
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1
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28
GATE2008IT30
Consider the function f(x) = x2  2x  1. Suppose an execution of the NewtonRaphson 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
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Oct 28, 2014
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IS&Software Engineering
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Ishrat Jahan
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gate2008it
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newtonraphson
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2
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29
GATE19962.5
NewtonRaphson iteration formula for finding $\sqrt[3]{c}$, where $c > 0$ is $x_{n+1}=\frac{2x_n^3 + \sqrt[3]{c}}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3  \sqrt[3]{c}}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3 + c}{3x_n^2}$ $x_{n+1}=\frac{2x_n^3  c}{3x_n^2}$
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Oct 9, 2014
in
Numerical Methods
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Kathleen
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gate1996
numericalmethods
newtonraphson
normal
outofsyllabusnow
0
votes
3
answers
30
GATE19952.15
The iteration formula to find the square root of a positive real number $b$ using the Newton Raphson method is $x_{k+1} = 3(x_k+b)/2x_k$ $x_{k+1} = (x_{k}^2+b)/2x_k$ $x_{k+1} = x_k2x_k/\left(x^2_k+b\right)$ None of the above
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Oct 8, 2014
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Numerical Methods
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gate1995
numericalmethods
newtonraphson
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