Matches in SemOpenAlex for { <https://semopenalex.org/work/W1539855477> ?p ?o ?g. }
- W1539855477 endingPage "711" @default.
- W1539855477 startingPage "417" @default.
- W1539855477 abstract "This chapter explains basic examples of wavelet methods in numerical analysis. It introduces the approximations and shows show the way they are related to decompositions in two elementary wavelet bases: the Haar system and the hierarchical Schauder basis. The chapter describes the decomposition and reconstruction algorithms that can be used to compute the coefficients of a function in these bases and it investigates the way these schemes can be generalized in a natural way to multivariate functions. The applications of these elementary tools to numerical analysis are also discussed in the chapter. The chapter also reviews some basic facts on the finite element discretization of a simple model second-order elliptic problem, which is known to yield an ill-conditioned system, and demonstrates the way multiscale decompositions can be used to design simple preconditioners and optimal iterative solvers. To generalize the previous multiscale schemes to multivariate functions, many different possibilities can be imagined. The chapter focuses on the two most frequently used approaches that are respectively based on tensor product and nested triangulations. For the sake of notational simplicity, these generalizations are described in the case of functions of two variables." @default.
- W1539855477 created "2016-06-24" @default.
- W1539855477 creator A5063162788 @default.
- W1539855477 date "2000-01-01" @default.
- W1539855477 modified "2023-09-30" @default.
- W1539855477 title "Wavelet methods in numerical analysis" @default.
- W1539855477 cites W1592007248 @default.
- W1539855477 cites W1608434507 @default.
- W1539855477 cites W1774981766 @default.
- W1539855477 cites W1966077455 @default.
- W1539855477 cites W1969011612 @default.
- W1539855477 cites W1970592267 @default.
- W1539855477 cites W1973513227 @default.
- W1539855477 cites W1975426136 @default.
- W1539855477 cites W1976194009 @default.
- W1539855477 cites W1980158900 @default.
- W1539855477 cites W1985629301 @default.
- W1539855477 cites W1987996534 @default.
- W1539855477 cites W1988406495 @default.
- W1539855477 cites W1989056711 @default.
- W1539855477 cites W1989594010 @default.
- W1539855477 cites W1990781410 @default.
- W1539855477 cites W1994336408 @default.
- W1539855477 cites W1997831216 @default.
- W1539855477 cites W2000430190 @default.
- W1539855477 cites W2001560283 @default.
- W1539855477 cites W2001672622 @default.
- W1539855477 cites W2002873284 @default.
- W1539855477 cites W2003989039 @default.
- W1539855477 cites W2004261587 @default.
- W1539855477 cites W2004766860 @default.
- W1539855477 cites W2009849678 @default.
- W1539855477 cites W2012164750 @default.
- W1539855477 cites W2013283293 @default.
- W1539855477 cites W2014051441 @default.
- W1539855477 cites W2015219711 @default.
- W1539855477 cites W2019113134 @default.
- W1539855477 cites W2020038074 @default.
- W1539855477 cites W2020919250 @default.
- W1539855477 cites W2021302824 @default.
- W1539855477 cites W2021589053 @default.
- W1539855477 cites W2022053762 @default.
- W1539855477 cites W2022270785 @default.
- W1539855477 cites W2025957493 @default.
- W1539855477 cites W2026741150 @default.
- W1539855477 cites W2028413588 @default.
- W1539855477 cites W2030934791 @default.
- W1539855477 cites W2032835894 @default.
- W1539855477 cites W2033686842 @default.
- W1539855477 cites W2034167241 @default.
- W1539855477 cites W2034419697 @default.
- W1539855477 cites W2036144352 @default.
- W1539855477 cites W2036242265 @default.
- W1539855477 cites W2036959719 @default.
- W1539855477 cites W2038192551 @default.
- W1539855477 cites W2039066931 @default.
- W1539855477 cites W2039921213 @default.
- W1539855477 cites W2039924562 @default.
- W1539855477 cites W2044084385 @default.
- W1539855477 cites W2045050233 @default.
- W1539855477 cites W2046064079 @default.
- W1539855477 cites W2046153167 @default.
- W1539855477 cites W2046680696 @default.
- W1539855477 cites W2050507755 @default.
- W1539855477 cites W2052197429 @default.
- W1539855477 cites W2053691921 @default.
- W1539855477 cites W2053954066 @default.
- W1539855477 cites W2056166036 @default.
- W1539855477 cites W2059914778 @default.
- W1539855477 cites W2062728462 @default.
- W1539855477 cites W2064216226 @default.
- W1539855477 cites W2064625750 @default.
- W1539855477 cites W2066531315 @default.
- W1539855477 cites W2066758297 @default.
- W1539855477 cites W2067862350 @default.
- W1539855477 cites W2071247981 @default.
- W1539855477 cites W2072595795 @default.
- W1539855477 cites W2076142036 @default.
- W1539855477 cites W2077070913 @default.
- W1539855477 cites W2081289139 @default.
- W1539855477 cites W2083214120 @default.
- W1539855477 cites W2085396618 @default.
- W1539855477 cites W2085456166 @default.
- W1539855477 cites W2086504382 @default.
- W1539855477 cites W2090055402 @default.
- W1539855477 cites W2090364262 @default.
- W1539855477 cites W2092891252 @default.
- W1539855477 cites W2093680258 @default.
- W1539855477 cites W2094585768 @default.
- W1539855477 cites W2095484060 @default.
- W1539855477 cites W2098914003 @default.
- W1539855477 cites W2100917607 @default.
- W1539855477 cites W2103504761 @default.
- W1539855477 cites W2107893295 @default.
- W1539855477 cites W2110157363 @default.
- W1539855477 cites W2111261932 @default.
- W1539855477 cites W2115566547 @default.
- W1539855477 cites W2117188745 @default.