Iterative Solvers for Discretized Equations MCQ

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• In incomplete Cholesky decomposition, the preconditioner matrix produced is ____________ (Note: L is the factorized lower triangular matrix and U is the factorized lower triangular matrix).
  ক

  UL’

  খ

  LU’

  গ

  LL’

  ঘ

  LL2
• Which of these methods is not restricted to symmetric positive definite matrices?
  ক

  The method of steepest descent

  খ

  Conjugate gradient method

  গ

  Bi-conjugate gradient method

  ঘ

  Gauss-Seidel method
• In which of these methods, after factorization, the pattern of zero elements in the combined L and U matrices the same as the original coefficient matrix?
  ক

  LU decomposition

  খ

  ILU decomposition

  গ

  ILU(0) decomposition

  ঘ

  ILU(1) decomposition
• What does the letter ‘I’ stand for in ILU decomposition problem?
  ক

  Inbuilt

  খ

  Incomplete

  গ

  Iterative

  ঘ

  Imbalanced
• Preconditioners improve ____________ of the coefficient matrix.
  ক

  sparsity

  খ

  rank

  গ

  spectral properties

  ঘ

  Singularity
• When compared to the Jacobi method, the Gauss-Siedel method ____________
  ক

  has better convergence and needs less memory

  খ

  has less convergence and needs more memory

  গ

  has less convergence and needs less memory

  ঘ

  has better convergence and needs more memory
• Consider the global matrix AΦ=b. What is the residual at the ith iteration? (Note: Φi is the value of Φ in the ith iteration).
  ক

  AΦi-1+b

  খ

  AΦi-1-b

  গ

  AΦi+b

  ঘ

  AΦi-b
• Consider the global matrix AΦ=b. Let the coefficient matrix A=M-N. At the ith iteration, the general form can be given as ______________ (Note: Φi is the value of Φ in the ith iteration).
  ক

  MΦi=NΦi-1+b

  খ

  MΦi=NΦi+b

  গ

  MΦi=NΦi-1-b

  ঘ

  MΦi=NΦi-b
• Let us divide the coefficient matrix into this form: A=D+L+U. Which of these matrices can be L in this equation?
  ক

  \(\begin{bmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 4 & 1 \end{bmatrix}\)

  খ

  \(\begin{bmatrix} 0 & 0 & 0 \\ 2 & 0 & 0 \\ 3 & 4 & 0 \end{bmatrix}\)

  গ

  \(\begin{bmatrix} 1 & 0 & 0 \\ 2 & 5 & 0 \\ 3 & 4 & 6 \end{bmatrix}\)

  ঘ

  \(\begin{bmatrix} 1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{bmatrix}\)
• Which of these statements is incorrect about iterative methods?
  ক

  Low computational cost

  খ

  Low computer storage

  গ

  Not suitable for sparse matrices

  ঘ

  Needs initial guess