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- W2000528287 abstract "Let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=x left-parenthesis p right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>p</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>x(p)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be the point which minimizes the residual of a linear system in the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=l Subscript p> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>l</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>{l_p}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> norm. It is known that under certain conditions <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=x left-parenthesis p right-parenthesis right-arrow x Superscript asterisk> <mml:semantics> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>p</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>x</mml:mi> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:msup> </mml:mrow> </mml:mrow> <mml:annotation encoding=application/x-tex>x(p) to {x^ast }</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the Chebyshev or <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=l Subscript normal infinity> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msub> <mml:mi>l</mml:mi> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>{l_infty }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> solution, as <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=p right-arrow normal infinity> <mml:semantics> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:mi mathvariant=normal>∞<!-- ∞ --></mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>p to infty</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. A differential equation describing <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=x left-parenthesis p right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>p</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>x(p)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is derived from which an iterative scheme is devised. A convergence analysis is given and numerical results are presented." @default.
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- W2000528287 date "1974-01-01" @default.
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- W2000528287 title "A new algorithm for the Chebyshev solution of overdetermined linear systems" @default.
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