Error analysis of a Monte Carlo algorithm for computing bilinear forms of matrix powers

In this paper we present error analysis for a Monte Carlo algorithm for evaluating bilinear forms of matrix powers. An almost Optimal Monte Carlo (MAO) algorithm for solving this problem is formulated. Results for the structure of the probability error are presented and the construction of robust and interpolation Monte Carlo algorithms are discussed. Results are presented comparing the performance of the Monte Carlo algorithm with that of a corresponding deterministic algorithm. The two algorithms are tested on a well balanced matrix and then the effects of perturbing this matrix, by small and large amounts, is studied.

Comparison of the computational cost of a Monte Carlo and deterministic algorithm for computing bilinear forms of matrix powers

In this paper we consider bilinear forms of matrix polynomials and show that these polynomials can be used to construct solutions for the problems of solving systems of linear algebraic equations, matrix inversion and finding extremal eigenvalues. An almost Optimal Monte Carlo (MAO) algorithm for computing bilinear forms of matrix polynomials is presented. Results for the computational costs of a balanced algorithm for computing the bilinear form of a matrix power is presented, i.e., an algorithm for which probability and systematic errors are of the same order, and this is compared with the computational cost for a corresponding deterministic method.

Valuation accuracy: reconciling the timing of the valuation and sale

Carsberg (2002) suggested that the periodic valuation accuracy studies undertaken by, amongst others, IPD/Drivers Jonas (2003) should be undertaken every year and be sponsored by the RICS, which acts as the self-regulating body for valuations in the UK. This paper does not address the wider issues concerning the nature of properties which are sold and whether the sale prices are influenced by prior valuations, but considers solely the technical issues concerning the timing of the valuation and sales data. This study uses valuations and sales data from the Investment Property Databank UK Monthly Index to attempt to identify the date that sale data is divulged to valuers. This information will inform accuracy studies that use a cut-off date as to the closeness of valuations to sales completion date as a yardstick for excluding data from the analysis. It will also, assuming valuers are informed quickly of any agreed sales, help to determine the actual sale agreed date rather than the completion date, which includes a period of due diligence between when the sale is agreed and its completion. Valuations should be updated to this date, rather than the formal completion date, if a reliable measure of valuation accuracy is to be determined. An accuracy study is then undertaken using a variety of updating periods and the differences between the results are examined. The paper concludes that the sale only becomes known to valuers in the month prior to the sale taking place and that this assumes either that sales due diligence procedures are shortening or valuers are not told quickly of agreed sale prices. Studies that adopt a four-month cut-off date for any valuations compared to sales completion dates are over cautious, and this could be reduced to two months without compromising the data.

Whose land was it anyway? The Crichel Down Rules and the sale of public land

The guiding principle of compulsory purchase of interests in land in England and Wales is that of fairness, best stated in the words of Lord Justice Scott in Horn v Sunderland Corporation when he said that the owner has “the right to be put, so far as money can do it, in the same position as if his land had not been taken from him”. In many instances, land acquired by compulsion subsequently becomes surplus to the requirements of the acquiring authority. This may be because the intended development scheme was scrapped, or substantially modified, or that after the passage of time the use of the land for which the purchase took place is no longer required. More controversially it may be that for ‘operational reasons’ the acquiring authority knowingly purchased more land than was required for the scheme. Under these circumstances, the Crichel Down Rules (‘the Rules’) require government departments and other statutory bodies to offer back to the former owners or their successors, any land previously so acquired by, or under the threat of, compulsory purchase.

Pianos for the people: the manufacture, marketing and sale of pianos as consumer durables, 1850-1914

During the second half of the nineteenth century, British society experienced a rise in real incomes and a change in its composition, with the expansion of the middle classes. These two factors led to a consumer revolution, with a growing, but still segmented, demand for household goods that could express status and aspiration. At the same time technological changes and new ways of marketing and selling goods made these goods more affordable. This paper analyzes these themes and the process of mediation that took place between producers, retailers, and consumers, by looking at the most culturally symbolic of nineteenth century consumer goods, the piano.