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## BIT Numerical Mathematics OnlineFirst articles

14.11.2018

### On Motzkin’s method for inconsistent linear systems

Iterative linear solvers have gained recent popularity due to their computational efficiency and low memory footprint for large-scale linear systems. The relaxation method, or Motzkin’s method, can be viewed as an iterative method that projects …

12.11.2018

### Rank one interval enclosure of the parametric united solution set

Consider linear algebraic systems $$A(p)x=b(p)$$ A ( p ) x = b ( p ) , where the matrix and the right-hand side vector depend linearly on a number of parameters $$p=(p_1,\ldots , p_K)^{\top }$$ p = ( p 1 , … , p K ) ⊤ that vary within given …

09.11.2018

### Accurate evaluation of Chebyshev polynomials in floating-point arithmetic

It is well-known that the Chebyshev polynomials $$T_n$$ T n and $$U_{n-1}$$ U n - 1 can be recursively expressed as linear combinations of $$T_{n-1}$$ T n - 1 and $$U_{n-2}$$ U n - 2 . We study floating-point implementations of these recurrences …

01.11.2018

### Mimetic properties of difference operators: product and chain rules as for functions of bounded variation and entropy stability of second derivatives

For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear systems …

17.10.2018

### Explicit computational wave propagation in micro-heterogeneous media

Explicit time stepping schemes are popular for linear acoustic and elastic wave propagation due to their simple nature which does not require sophisticated solvers for the inversion of the stiffness matrices. However, explicit schemes are only …

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BIT was started by Carl Erik Fröberg in 1961. The name is an acronym for "Tidskrift för Informationsbehandling" read backwards. From the outset, a wide area of computer science and technology was covered, but since 1992 the focus has been on Numerical Mathematics.

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Bo Kågström, Umeå University, appointed by IVA, Kungliga Ingenjörsvetenskapsakademien, Sweden
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BIT publishes original research papers in the rapidly developing field of numerical analysis. The essential areas covered by BIT are development and analysis of numerical methods as well as the design and use of algorithms for scientific computing. Topics emphasized by BIT include numerical methods in approximation, linear algebra, and ordinary and partial differential equations, but BIT also publishes papers in areas such as numerical functional analysis and numerical optimization.

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