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*** 4.14. Suppose the eigenvalues of a symmetric matrix A satisfy A₁ > A₂ > ≥ An-1 > An > 0. To calculate A₁, the power
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- 4 14 Suppose The Eigenvalues Of A Symmetric Matrix A Satisfy A A An 1 An 0 To Calculate A The Power 1 (28.73 KiB) Viewed 16 times
*** 4.14. Suppose the eigenvalues of a symmetric matrix A satisfy A₁ > A₂ > ≥ An-1 > An > 0. To calculate A₁, the power method is going to be applied to the shifted matrix B= A - WI. (a) What condition(s) must be imposed on w so the method will converge to X₁. (b) Explain why the choice w = (A2+ An)/2 will result in the fastest conver- gence of the power method.