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- W158972990 abstract "Publisher Summary This chapter focuses on the main diagonal of a bi-infinite band matrix. It is shown how to single out a particular diagonal of a bi-infinite band matrix A as its main diagonal, using the de-composition of the solution set of Ax = 0 into those that are bounded at ∞ and −∞. As an application, it is proved that the inverse of the coefficient matrix for the system satisfied by the B-spline coefficients of the cubic spline interpolant at knots is checkerboard and that, under certain assumptions, the local mesh ratio must be bounded. The study of approximation by splines on a bi-infinite knot sequence leads to linear systems Ax = b with a banded bi-infinite coefficient matrix A. For matrices that are not triangular with triangular inverse, it is much more difficult to ascertain whether or not they even have a main diagonal." @default.
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- W158972990 date "1980-01-01" @default.
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- W158972990 title "WHAT IS THE MAIN DIAGONAL OF A BIINFINITE BAND MATRIX?" @default.
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- W158972990 doi "https://doi.org/10.1016/b978-0-12-213650-4.50008-8" @default.
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