Basic text for graduate and advanced undergraduate deals with search for roots of algebraic equations encountered in vibration and flutter problems and in those of static and dynamic stability. Other topics devoted to matrices and eigenvalue problems, large-scale linear systems, harmonic analysis and data analysis, more.
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accuracy adjoint algebraic equation amplitudes analysis analytical applied approximation arbitrary assume base vectors becomes boundary conditions Chebyshev polynomials coefficients coeﬂicients columns complex numbers components convergence data points deﬁned deﬁnite integrals derivative determined diagonal difference differential equation dot product eigenvalue problem eigenvectors elements end points equidistant error estimate evaluation example ﬁgures ﬁnal ﬁnd ﬁnite ﬁrst ﬁve Fourier series frequency function f fundamental Gaussian quadrature given function gives gonal Hence inﬁnite inﬂuence interpolation interval inverse Laplace transform Legendre polynomials limit linear system mathematical matrix method modiﬁed movable strip multiply noise obtain operation ordinates original orthogonal oscillations principal axes procedure quadratic surface range reference system replaced result right side roots satisﬁed signiﬁcance Simpson’s sine skew-angular smoothing solution solving symmetric symmetric matrix Taylor expansion Taylor series tion triangular matrix trigonometric trigonometric interpolation values variable vectors weight factor zero