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Sections 4.3 (The master method) and 4.4 (Proof of the master theorem), pp. 73–90. Michael T. Goodrich and Roberto Tamassia. Algorithm Design: Foundation, Analysis, and Internet Examples. Wiley, 2002. ISBN 0-471-38365-1. The master theorem (including the version of Case 2 included here, which is stronger than the one from CLRS) is on pp. 268 ...
In model theory, a branch of mathematical logic, the diagram of a structure is a simple but powerful concept for proving useful properties of a theory, for example the amalgamation property and the joint embedding property, among others.
In computer science, the Akra–Bazzi method, or Akra–Bazzi theorem, is used to analyze the asymptotic behavior of the mathematical recurrences that appear in the analysis of divide and conquer algorithms where the sub-problems have substantially different sizes.
the logarithmic cost model, also called logarithmic-cost measurement (and similar variations), assigns a cost to every machine operation proportional to the number of bits involved The latter is more cumbersome to use, so it is only employed when necessary, for example in the analysis of arbitrary-precision arithmetic algorithms, like those ...
In mathematics, a theorem that covers a variety of cases is sometimes called a master theorem. Some theorems called master theorems in their fields include: Master theorem (analysis of algorithms), analyzing the asymptotic behavior of divide-and-conquer algorithms; Ramanujan's master theorem, providing an analytic expression for the Mellin ...
Digital antenna array (DAA) is a smart antenna with multi channels digital beamforming, usually by using fast Fourier transform (FFT). The development and practical realization of digital antenna arrays theory started in 1962 under the guidance of Vladimir Varyukhin ( USSR ).
The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries = =. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop:
The bracket integration method (method of brackets) applies Ramanujan's master theorem to a broad range of integrals. [7] The bracket integration method generates the integrand's series expansion , creates a bracket series, identifies the series coefficient and formula parameters and computes the integral.