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31 lines
1.2 KiB
Markdown
31 lines
1.2 KiB
Markdown
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# ENUME_Project1
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A Numerical Method project cointaining 4 tasks.
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## 1.
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Write a program finding macheps in the MATLAB environment on a lab computer or your
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computer.
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## 2.
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Write a general program solving a system of n linear equations Ax = b using the indicated
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method Apply the program to solve the system of linear equations for given matrix A and vector b, for increasing numbers
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of equations n = 10,20,40,80,160,… until the solution time becomes prohibitive (or the
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method fails), for:
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### a)
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Aij { for i = j -> 13, for i = j-1 or i = j+1 -> 4, other -> 0 \
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Bi = 2.4 + 0.6i, \
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i,j = 1..n;
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### b)
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Aij = 4/[5(i + j – 1)], Bi = 1/(2 i), i – odd; Bi = 0, i – even, i, j = 1,…,n;
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## 3
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Write a general program for solving the system of n linear equations Ax = b using the
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Gauss-Seidel and Jacobi iterative algorithms. Apply it for the system: \
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13x1 + 2x2 – 8x3 + x4 =16 \
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x1 + 10x2 + 5x3 – 2x4 = 24 \
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6x1 + 2x2 – 23x3 + 15x4 = 184 \
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x1 + 2x2 – x3 + 13x4 = 82
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## 4
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Write a program of the QR method for finding eigenvalues of 5×5 matrices: \
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a) without shifts; \
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b) with shifts calculated on the basis of an eigenvalue of the 2×2 right-lower-corner
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submatrix.
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