Wilkinson matrix

In linear algebra, Wilkinson matrices are symmetric, tridiagonal, order-N matrices with pairs of nearly, but not exactly, equal eigenvalues.^[1] It is named after the British mathematician James H. Wilkinson. For N = 7, the Wilkinson matrix is given by

{\begin{bmatrix}3&1&0&0&0&0&0\\1&2&1&0&0&0&0\\0&1&1&1&0&0&0\\0&0&1&0&1&0&0\\0&0&0&1&1&1&0\\0&0&0&0&1&2&1\\0&0&0&0&0&1&3\\\end{bmatrix}}.

Wilkinson matrices have applications in many fields, including scientific computing, numerical linear algebra, and signal processing.

References

↑ Wilkinson (1965). The Algebraic Eigenvalue Problem. Oxford University Press. ISBN 0-19-853418-3.

Numerical linear algebra

Key concepts	Floating point Numerical stability

Problems	Matrix multiplication (algorithms) Matrix decompositions Linear equations Sparse problems

Hardware	CPU cache TLB Cache-oblivious algorithm SIMD Multiprocessing

Software	BLAS Specialized libraries General purpose software

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