Matrix iterative analysis (2nd edn)

By S. Abbott. Mathematical Gazette, 2000

699 citations recorded by the source corpus.

a 'sleeper', receiving only modest attention for 50 years before emerging as a cornerstone of communications engineering in more recent times. Roughly one in six of Walsh's 281 publications are included, photographically reproduced. Reproduction is excellent except for one paper from 1918. The book also reproduces three brief papers about Walsh and his work, by W. E. Sewell, D. V. Widder and Morris Marden. The first two were written for a special issue of the SIAM Journal celebrating Walsh's 70th birthday; the third is an obituary.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/7d470b65a6f3232082f45b2728df44fcfec40726

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Citations in the corpus

• Numerical solution of singularly perturbed convection-diffusion-reaction problems with two small parameters (2015, neutral): “Proof The stiffness matrix associated with the discrete operator (I +Δt LM ) at every time level tn+1 is an irreducibly diagonally dominant M-matrix [28] and thus it has a nonnegative inverse.”
• On best rank one approximation of tensors (2011, neutral): “Then this iteration is the block Gauß-Seidel iteration, see for example, [12], applied to the linear system H D 0 with the block symmetric matrix H , that is,”
• Numerical methods for controlled Hamilton-Jacobi-Bellman PDEs in finance (2007, background): “It is also useful to note that [I − (1− θ)An(Qn)] is an M-matrix [47].”
• Proximal Splitting Methods in Signal Processing (2009, neutral): “This type of scheme is known as a forward–backward splitting algorithm for, using the terminology used in discretization schemes in numerical analysis [132], it can be broken”
• Network Topology and Communication-Computation Tradeoffs in Decentralized Optimization (2017, methodology): “ble. Intuitively, Eq. (12) takes a lazy Metropolis update and accelerates it by adding an extrapolation term. Strategies of this form are known as over-relaxation in the numerical analysis literature [38] and as Nesterov acceleration in the optimization literature [39]. On a non-technical level, the”