Algorithms: Their Complexity and EfficiencyThis revision of the successful first edition develops and teaches fundamental techniques for obtaining efficient algorithms to solve problems. Updates include important advances in the computational complexity of matrix multiplication and completely new chapters on sorting and searching. Provides a systematic and in-depth study of the computational complexity of a wide range of practical algorithms, both numerical and non-numercal. Considers numerical algorithms in terms of both computational speed and computational accuracy performance. Provides excercises at the end of each chapter, some with answers, to provide examples of concepts. |
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a₁ arithmetic operations array assume average number b₁ Belaga binary search binary tree coefficients complexity computed consider convergence defined denotes derivatives discrete Fourier transform distribution efficient elements enddo endif equations error analysis evaluate a polynomial evaluation algorithm example external sorting f(xi FFT algorithm formula Gaussian elimination given hash function heapsort Horner algorithm ill-conditioned initial runs input insertion integer interpolation inverse iterative method linear log2 matrix multiplication minimum number node number of arithmetic number of comparisons number of multiplications numerical stability obtained optimal p₁ parameters permutation pivot polynomial form polyphase merge polyvalue preprocessing probes problem Quicksort root round-off errors search key search tree secant method sequence solution solve step Strassen algorithm tapes theorem total number two-way merge sort V₁ vector Winograd Xi+1