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## BIT Numerical Mathematics OnlineFirst articles

31.08.2020

### Simple formula for integration of polynomials on a simplex

We show that integrating a polynomial f of degree t on an arbitrary simplex (with respect to Lebesgue measure) reduces to evaluating t homogeneous related Bombieri polynomials of degree $$j=1,2,\ldots ,t$$ j = 1 , 2 , … , t , each at a unique …

26.08.2020

### Optimal quadratic element on rectangular grids for problems

In this paper, a piecewise quadratic finite element method on rectangular grids for $$H^1$$ H 1 problems is presented. The proposed method can be viewed as a reduced rectangular Morley element. For the source problem, the convergence rate of this …

20.08.2020

### Verified inclusions for a nearest matrix of specified rank deficiency via a generalization of Wedin’s theorem

For an $$m \times n$$ m × n matrix A, the mathematical property that the rank of A is equal to r for $$0< r < \min (m,n)$$ 0 < r < min ( m , n ) is an ill-posed problem. In this note we show that, regardless of this circumstance, it is possible to …

11.08.2020

### Randomized Kaczmarz with averaging

The randomized Kaczmarz (RK) method is an iterative method for approximating the least-squares solution of large linear systems of equations. The standard RK method uses sequential updates, making parallel computation difficult. Here, we study a …

07.08.2020 Open Access

### An accurate integral equation method for Stokes flow with piecewise smooth boundaries

Two-dimensional Stokes flow through a periodic channel is considered. The channel walls need only be Lipschitz continuous, in other words they are allowed to have corners. Boundary integral methods are an attractive tool for numerically solving …

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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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