GATE 2009
1. Geophysical inverse problems are described by
(a) Fredholm's integral equation of first kind
(b) Fredholm's integral equation of second kind
(c) Volterra's equation of second kind
(d) Legendre equation
2. Spot the ANN method from the following:
(a) Singular value decomposition
(b) monte-car lo technique
(c) Ridge regression procedure
(d) Back propagation technique
3. The concept of resolving kernel is used in
(a) Tikhonov's regularization method
(b) Ridge regression method
(c) Backus-Gilbert method
(d) Simulated annealing method
GATE 2010
1. Unguided random-walk inversion technique signifies
(a) Genetic algorithm
(b) Simulated annealing
(c) Monte Carlo inversion
(d) Metropolis algorithm
2. If m represents the number of model parameters, d the number of data points and p the rank of matrix to be inverted, then which of the following defines an under determined system?
(a) m < d and p = d
(b) m > d and p = d
(c) m = d and p = d
(d) m < d and \(p \neq d\)
GATE 2011
1. The least squares generalized inver se of an overdetermined problem is expressed as
(a) \((GTTG)^{-1}G^T\) (b) \((G^T G)^{-1}\)
(c) \(G^T (GG^T)^{-1}\) (d) \((GG^T)^{-1}\)
GATE 2012
1. The solution to the purely under-determined problem Gm = d is given by
(a) \((G^TG)^{-1} G^Td\)
(b) \((G^TG)^{-1} Gd^T\)
(c) \(G^T(GG^T)^{-1}d\)
(d) \(G^Td(GG^T)^{-1}\)
2. Given the following matrix equation: \(A_{m\times n} X_{x\times1} = b_{m\times1}\) the nature of this system of equation is
(a) over-determined if m > n
(b) under-determined if m < n
(c) even-determined if m = n
(d) determined by the rank of the matrix A
GATE 2013
1. A singular value of an \(m \times n\) matrix, A, is defined as
(a) positive square root of eigenvalue of \(AA^T\)
(b) modulus of eigenvalue of A
(c) eigenvalue of \(A^TA\)
(d) square of eigenvalue of A
2. In an ill-posed geophysical inverse problem, stated as non-singular matrix equation, the magnitude of determinant of the coefficient matrix is
(a) large (b) zero (c) near zero (d) very large
GATE 2014
1. Consider the four systems of algebraic equations (listed in Group I). The systems (Q), (R) and (S) are obtained from (P) by restricting the accuracy of data or coefficients or both respectively, to two decimal places.
Match these systems to their characteristics (listed in Group II)
Group I Group I I
P. x+ 1.0000y = 2.0000 1. instability
x+1.0001y = 2.0001
Q. x+ 1.0000y = 2.00 2. inconsistency
x+1.0001y = 2.00
R. x+ 1.00y = 2.0000 3. non-uniqueness
x+1.00y = 2.0001
S. x+ 1.00y = 2.00 4. exact
x+1.00y = 2.00
(a) P-1; Q-4; R-3; S-2
(b) P-4; Q-1; R-2; S-3
(c) P-4; Q-1; R-3; S-2
(d) P-1; Q-4; R-2; S-3 50.
2. The eigenvalue (\(Lambda) and eigenvector (U) matrices for singular value decomposition of the matrix
respectively are